Adaptor Strategy: Foresight

PROBING, ADAPTING, AND STEERING

The interpretation of our special control engineering ingredient of time-varying parameters α(T) has come quite a long way: from coefficients in a time-series model; to features and elements in a design space that are important to the makeup of the system; to resilience, and to bounce forward. But when all was said and done in respect of the exceptionalism of the Adaptor strategy — in the two Parts of the article and the Link between the two — some loose ends were left to be tied up. For one thing, we never properly hinted at how exactly we might deal with those (very big) “somehows” integral to the Adaptor’s diagnostic capabilities in discharging its switching function.

What is more, we made no use of a rather special segment of adaptive control theory: the joint probing and steering of “dual adaptive control”.

Three Models and Their Use in the Adaptor’s Diagnostic Work

Somehow something has to be done about these issues:

  • Diagnosing the nature of the risk environment surrounding the company, i.e., determining the season of risk;
  • Sensing and detecting an imminent or actual transition in that risk environment; and
  • Diagnosing which strategy should be deployed into the driving seat to cope with the new, post-transition season of risk.

The outcome of the diagnosis is to switch (or not): between the autopilot of the current (about to pass) season of risk and the autopilot of the next (about to arrive) season. It is a peremptory action, quite abrupt. And one therefore to be questioned, for that very reason.

To serve the purposes of the Adaptor’s diagnosing, three domains of modelling can be listed:

  • One for what emanates from the “Environment” of the “System” in the basic feedback control diagram of Figure1 in Part I, i.e., one for the pattern of the disturbance stream characterizing the company’s risk environment, d(t). This would take the form of a univariate time-series model.
  • One for the company’s non-executive processing procedures in the O block of the system. This would be typically an input-output model relating the inputs d(t) and company decisions u(t) to the company’s output performance y(t). Again, refer to Figure 1, Part I.
  • A third for the company’s risk-coping strategy, i.e., its executive decision rule(s) embedded in the controller K block of the system. This would be in the form of another input-output model relating the (fed-back) mismatches as the inputs — these being a function of the y(t) (and, somewhat “off-stage” in Figure 1, the presumed seasonally time-invariant company “wants” yw) — to the decisions u(t) (as outputs).[1]

For each domain, each category of model is presumed to be so sufficiently simple as to be known to be wrong, in general. The structure of the model does not match the structure underlying the pattern of the d(t), or those underlying the dynamic behaviors of the O and the K in the real world. But the structure of the model can continually be made right for the times; and how it is continually being rectified is fruitfully revealing.

In formal, technical terms, the models we have in mind are to be employed as follows:

  • To determine whether the statistical, ergodic or non-ergodic, nature of the risk streams d(t) impinging on the company from the outside are changing qualitatively. In this, the recursive estimates for the respective domain model’s time-varying parameters αd reveal something about the essential structure of the system’s “Environment”, which inferred structure is indicative of which of the four seasons of risk the company is experiencing.[2]
  • To determine whether what is inside the decision-strategy K block within the system, when confronted with the incoming d(t), comports with what should be being achieved with the current company operating procedures in the O block, hence apparent in the resulting outcomes y(t). The diagnostic work here entails inspection of the patterns in the recursive parameter estimates of the two other domain models: those of the input-output behaviors of the O and the K, respectively the behaviors of the αO and the αK. These are basic indicators of what might be wrong (or right) about what resides within the makeup of the “System”.

We bestow upon the Adaptor an obsession: with what is changing with slow time; with change and evolution, that is, in the underlying structure of how the company’s risk environment is impinging on its operations. In the second of the two tasks of diagnosis, therefore, the Adaptor is interested in whether (and how) company decision strategy is diverging from what should be being done to attenuate the qualitatively changing impacts of the risks on desired company performance. The Adaptor’s goal in this is the apprehension of a failing constituent — a failing structural member in the various α (such as a failing component of the autopilot in the driving seat) — in the interacting complex of risk environment (d), strategy (K block), and company operational (O block) performance.

This focus of the Adaptor — on affairs, in effect, in the parametric space of α — is distinctively different from the focus of the other basic four rationalities, whose immediate focus is on risk-coping, each in its own distinctively different way.

FORESIGHT AND “PREDICTABILITY” OF SEASONAL CHANGE

In the motivating “tutorial” case of the guided missile (in the Link between Parts I and II), the structure of an in-line, on-board model can (as we have said) be made “right” for the times, for the present moment (above all), through the flexing and bending of the model structure. Which bending and flexing are enabled by the capacity to estimate the parameters at each decision point, to re-estimate them at the next point, and yet again (and again), ergo to reconstruct the α(T) as they evolve. The recursive algorithms are continually changing the values of the parameters so that the model matches the empirically palpable structure of the data, in the here and now. The model embodies the best current snapshot of the system’s dynamics. The tutorial of the guided missile serves to illustrate the general principle.

The essential task of the Adaptor is therefore to examine and interpret the nature of the variations in the αd(T) as they evolve: as reflections of the structure (trend, variance, auto-correlation, amplitude) of the patterns in the stream of risks and disturbances d(t), as they evolve through one season and into another. If and when the αd(T) trajectories prompt the Adaptor to conclude that a seasonal transition in the structure of the d(t) is occurring, throwing the switch is imminent.

For the case of peremptory switching in RA for ERM, the switching is between one time-invariant decision strategy and another: substituting one occupant of the K block for another. It is an abrupt swap, in but an instant.

But that is only half of the task, because the type of the about-to-arrive season has to be discerned, so that the right autopilot can be switched into the company driving seat. Addressing this other half of the switch-throwing decision is yet more of a challenge than that of the first part. Resolving it might run as follows.

Employing Foresight in Parametric Space — Benefitting from Slow Time

Seasons of risk are manifest in the system’s variables, notably the d(t), but also (under the second of the Adaptor diagnostic tasks using models) in the y(t) and the u(t), when these are analyzed alongside the d(t). The dynamics of these three sets of variables are manifest essentially in quick time t. Evidence of changes in the season of risk, in particular, is revealed in the dynamics of the reconstructed trajectories of the model’s α(T), which, in contrast, are apparent in slow time. There are two implications of this bifurcation of quick and slow time.

First, predictability of the behavior in slow time of the parameters α(T) over a longer-term horizon is probably superior to the predictability of d(t) (and the other variables) over this same longer-term span. To express this another way around, if we bound the longer-term span as that between points T and T+1 in slow time — and the companion conceptual shorter-term span in quick time as that between t and t+1 — then the predictability of d(t+1) given d(t) is probably roughly comparable to that of α(T+1) given α(T).[3] Expressed yet another way, extrapolation of the supposed trends in the α(T), from the current to the next season in slow time — crucially, therefore, over several, if not many, decision points in quick time t (to t +1, t+2, t+3, and so on) — should be more trustworthy than extrapolation of the high-frequency flutter in the d(t).

The implication is that migration (or transition) from one to another season, which is the nub of the challenge, is more likely to be correctly diagnosed through the parameters α(T) than through any other operational factors, anchored as they are in t.[4]

“Predictable” Migration Past Tipping Points

The second implication arising from the split, between variables varying in quick time t and the model parameters varying in slow time T, is this. A gradual, incremental, yet extrapolatable change in a parameter α may prompt a qualitative, perhaps abrupt shift in the behavior of the quick-time variables.

For instance, studies of the weakening restorative forces in national economies (as addressed in the Link) invoke catastrophe theory to demonstrate conceptually how GDP — the quick-time output y(t) variable of the system — may change qualitatively when the illustrative hypothetical control parameter changes its value by a vanishingly small amount. For it has passed one of those “tipping points”, such that the quick-time pattern of the y(t) of GDP suddenly changes distinctively, from, say, low-amplitude, lower-frequency oscillations to high-amplitude, higher-frequency oscillations.

In the familiar economic context of RA for ERM, it is not too difficult to equate such a tipping point to the qualitative and especially dramatic inflexion in the relevant d(t) or y(t) between the seasons of boom and bust.

Our argument is that whatever it might be in the makeup of the system’s risk environment that generates the disturbance stream d(t), the occurrence of such significant seasonal transitions in the prevailing quick-time pattern of d(t) may be due to but a very small change — within a more predictable, slow-time trend — in the αd(T). Thus, if the Adaptor has to hand a sense of this drift in αd(T) over the past and up to the present, the type of the risk season towards which the system’s environment is tending in the future may be identifiable. Since a specific decision strategy (maximizer, manager, etc.) is known by the Adaptor to be so well suited to that imminent and qualitatively different season, the switch is thrown: from the current autopilot in the driving seat to the newly diagnosed one.

Abrupt Jumps in Parameter Space αK

In the parameter space of the (controller) K block, affairs are to be shifted — “just like that” — from the location of one “pole” to another in the abstract parameter space of K, i.e., that specifically of αK.[5] Each of the four such poles denote the particular parameterization of the model of any one of the four risk-coping strategies: maximizer, manager, conservator, pragmatist. Each pole corresponds to a time-invariant αK, with, of course, a qualitatively different αK for each strategy’s version of the K model.

In the parameter volume (space), therefore, think of it this way. There are four distinctly different locations of the archetypal poles (snapshots) in the αK space corresponding to the four time-invariant structures of the archetypal strategies. The Adaptor’s switching of decision strategies at the transitions between seasons is thus visually equivalent to an abrupt jump from one to another pole in the αK space.

But there is a caveat.

Adaptor Nurturing: The Prerequisite of Switching

The switching function of the Adaptor in RA for ERM can only succeed provided the unequivocal viability of each of the four risk-coping strategies (maximizer, manager, conservator, pragmatist) is nurtured throughout all time. Otherwise, should any one of these rationalities go extinct, the Adaptor may call for the switch, yet no fresh vibrant autopilot for the new season is there to jump into the company driving seat at a moment’s notice.

The operation, of the switching function today, relies essentially on the prior, foregoing investment of the nurturing function. The nurturing maintains the viability of affairs within the makeup and fabric of the business. Nurturing maintains the business’s human resources (as elaborated in Part II).

Think of it this way. If the hatches securing the vessel’s cargo holds have not been suitably maintained — if over time their hinges have rusted such that the hatches remain open and unmovable, or (worse still) they have corroded and the doors have fallen off — they will not be there for battening down the hatches when the storm hits.

The nurturing function of the Adaptor sustains the fourfold variety of decision-making strategies, precisely the “variety” intended in the title of our (2021) SoA Research Report. Visually, the foursome are the four distinctly separate poles in the parameter space αK of the accompanying K-block model.

And just in case, let us emphasize once more that we are not interested in deploying our special ingredient of the time-varying parameters α(T) to track the noise in the data (on the d’s and the y’s), but in revealing any underlying structural change, diagnosing it, even anticipating whither it might be headed. Ergo, we are not interested in the α(T) as glorified fiddle factors. But we are now interested in the variety of the peremptory switching being rendered as the variability over slow time of the structure of just a single notional model.[6]

SMOOTH ADAPTATION OF STRATEGY

Peremptory switching, between one decision strategy and another, strongly implies this: that seasons of risk themselves change abruptly, from moderate to boom to bust to uncertain, or whatever. But is this really so?

There is also this. Qualitative change in the pattern of the external risk environment (in the d) is not the sole motivator of the need to adapt strategy in the controller K block of the system (of Figure 1 in Part I). Changes in the structure of the system’s operations O block may also necessitate the adaptation of strategy.

As in the Link, let us again use the guided missile and GDP in a macro-economy to introduce the relevance to RA for ERM of what is entailed.

From Guided Missiles …

The operations (O) block of the missile houses its propulsion unit. The controller (K) block houses the control rule for guiding the missile.

Once fired, structural change is inevitable in the system of the missile. Its on-board fuel is being expended; its mass is accordingly declining over time. What is in the O block of the missile is changing with time; we have the time-varying O-block parameters αO(T). The missile’s open-loop dynamic behavior — as encapsulated in its hypothetical unforced response, RT(t) — is therefore changing over time. In other words, the intrinsic properties of the stability-instability of the missile in the face of perturbation are changing with macro time T. And, as before, the subscript T in the perhaps awkward notation of RT(t) signals the fact that this intrinsic property (the system’s unforced response) is changing relatively slowly with time.

Yet to proceed with minimum deviation along its path, the missile needs controlling such that its closed-loop response to atmospheric perturbation remains unchanged. Its controlled, closed-loop response to identical buffeting by the atmosphere later on, should be the same as its closed-loop response earlier. Its closed-loop RLater(t) should be the same as its closed-loop REarlier(t). To enable this, the structure of what is in the missile’s controller (K) has to be adapted with time, as facilitated by the special ingredient of the control (decision) parameters αK(T). Such a style of control is adaptive and it is self-tuning. The αK(T) is being changed in sympathy with the best current snapshot of the missile’s intrinsic dynamic behavior, i.e., its open-loop RT(t). In turn, this snapshot is being continually updated in real-time (t) — it is ever tuning itself — by means of the recursively estimated parameter values substituted into the in-line, on-board model(s), as approximations of the missile’s observed movements.

To proceed thus towards an insurance company, let us return to the case of the weakening restorative forces in a national economy, which was used as another tutorial case study in the Link.

… To GDP in an Economy …

If a national economy were to submit itself to being controlled as though a guided missile (if indeed!), the adaptive αK(T) device could be employed so as to include compensation for the weakening restorative forces within the economy, i.e., the changes over time in the O-block parameters αO(T).

The test is this. The “storm” (the disturbance d) that induced the 1929 crash, is to be applied (in the imagination) to a national economy in 1959 and again in 1989. But by 1959 the lesson of 1929 has been learned. A self-tuning macro-economic control scheme (a policy) is accordingly in place; given is the presumption that the restorative forces in an economy are ever weakening over the years and decades. The structure of the policy (αK(T)) will continually be adapting to cover for these weakening forces (the αO(T)).[7] In other words, with the “right” (adaptive) national economic control measure being exercised from the 1930s onwards, the closed-loop response of the national economy to a crash in 1989, i.e., its closed-loop R1989(t), should be every bit as successful as the hypothetical closed-loop R1959(t) response.

Bounce back in 1989 is as swift and direct as bounce back was in 1959 — irrespective of the progressive weakening of the restorative forces at work in the economy. Citizens of this national economy would in 1959 and 1989 sense far less of the shock they would have suffered in 1929. There would be none of any wasteful or disruptive under- or over-shoot in the smooth and direct bounce-back — despite the progressive weakening of the restorative forces in the economy.

… And the Take-home Message for RA in ERM for Insurers

To summarize what has been learned from the guided missile and its national economic counterpart, we have this.

In those two tutorials, there is never any abrupt, discontinuous switching, such as that among the fourfold plurality of the four basic risk-coping strategies in RA for ERM. Instead, a singularly structured strategy is prosecuted.  However, we note that the adaptation is not prompted by any qualitative change in the system’s external (risk) environment (the d(t)). It is motivated by change in the structure of the system’s operations, i.e., by the αO(T) in its O block.

While the structure of the strategy remains fixed, its parameterization is adapted. That adaptation describes a continuous, smoothed trajectory in the K-block parameter space of αK. Indeed, let us think of this smoothed, non-disjoint αK(T) parameterization of a single structure of risk-coping strategy — located inside the K-block of the lower Strategy segment of the cascade control scheme (in Figure 3 of Part I of this article) — as a “surrogate”. It has replaced, if not usurped, the switching function once (notionally) discharged by the Adaptor rationality in the upper Adaptation segment of Figure 3 (Part I).

Visually, we may say that the previous “variety” of the four quite distinct poles distributed about the K-block parameter space has, in this now self-tuning, adaptive decision strategy, been rendered the “variability” over time of a single decision strategy, whose precise location moves smoothly around the parameter space, as αK(T), with essentially no abrupt jumps. It describes a trajectory over time therein. Any particular location on that trajectory is the decision strategy’s particular parameterization for the corresponding, present moment (in t) of decision making.

This is not complicated stuff. Just three or four model coefficients can allow the controller decision model to evolve through the four risk-coping strategies of a business, as elaborated further in our (2021) SoA Research Report. In particular, basic feedback control comes with an equally classical “compound” form of action, in which we have this. The outgoing decision (u) is a compound of three components: a portion that is proportional (P) to the magnitude of the ingoing mismatch (between what is “wanted” and what is “got”); another portion proportional to the integral (I) over time of the mismatch; and a third component that is proportional to the derivative (D) of the mismatch over time. This so-called PID control, moreover, can be shown to have a parallel in the plural “social constructions of time” of each rationality behind each risk-coping strategy. Which is to say, this social construction of time in Cultural Theory is integral to the constructed world — the Myth — upheld by each rationality.

INTERACTIONS AMONG THE RATIONALITIES

Hybrid Strategies in RA for ERM

The self-tuning αK(T) is changing continuously and smoothly (never disjointedly). As it does so, it passes among and through the neighborhoods of the four distinct poles (in the αK space) of the archetypal snapshots of the maximizer, manager, conservator, and pragmatist strategies. Consequently, in RA for ERM we could have a decision strategy that, in principle, is ever changing slowly through not only the four archetypal snapshots themselves, but also all points in between. At times, therefore what is in the driving seat of company decision-making may be a pure archetypal strategy and at other times a hybrid or blended strategy, for example, of conservator-pragmatist strategy, or a manager-maximizer, or whatever. The compound strategy of PID control embraces just the same, not least when interpreted according to the controller’s social construction of time.[8]

More than one pair of hands, or fingers and thumbs from different pairs of hands, may be gripping the steering wheel. More than one rationality may occupy the K block in the Strategy segment of the cascade control scheme at one and the same time (we are referring again to Figure 3 in Part I). Indeed, under such adaptive control with the switching function delegated to the surrogate of αK(T), the fifth Adaptor rationality is absent from the picture. There is no switching as such to be exercised. Nonetheless, we presume the Adaptor will be otherwise gainfully engaged, not least in discharging its nurturing function.

Adaptors Nurture While Others Cope with Everyday Risk

The development of RA for ERM was driven by the need for rational adaptability in the presence of seasonal, qualitative change in the nature of the d, not the O that motivated the adaptive K in the control engineering of a guided missile. But the structure of an insurer’s operations (the content of its O block) could well be changing, within one and the same unchanging season of risk, not least because of the interventions of the Adaptor.

Suppose the Adaptor is engaged in its nurturing function. A steady, if not stealthy, structural change reflected in the αO(T) may result from the Adaptor’s continual investment in the human and material resources allocated to the claims processing of the O block. Re-training of personnel and upgrading of supporting IT facilities come to mind. As a result, “turn-around time” in the O block — something akin to the O block’s intrinsic open-loop dynamic behavior symbolized as RT(t) — might be becoming progressively faster.

Suppose further it happens to be the risk season of bust, for example, such that the conservator strategy of premium-setting is firmly ensconced in the company’s driving seat, hands on the steering wheel. In this case, the pattern or structure of the risk stream (d(t)) is not changing qualitatively. The conservator is right to insist that it is the one to be doing the driving.

Yet for better or for worse, as this conservator sees it, the Adaptor is changing the intrinsic stability-instability of the company. The company’s αO(T) is changing; the makeup of company operations is continually being refurbished, albeit relatively slowly. Should the conservator adapt its risk-coping strategy? Could it? Would it?

Could the conservator do so even to a relatively minor extent: to benefit, therefore, from some learning (up to a point); in its own quite distinctive way, i.e., different from the ways of learning of the maximizer, the manager, and even the pragmatist; hence adjusting its premium-setting strategy? Because technically the risk-coping strategy of the conservator should be being adapted: if the αO(T) is changing, then so too should the conservator’s αK, albeit strictly within but the local vicinity of its corresponding archetypal pole in the αK parameter space. Strategy adaptation would be but minor: in small increments of δαK(t), we might write, within the vicinity of the pole (in our illustration) of the archetypal snapshot of the αKConservator.

Or would the conservator view the Adaptor as that fifth meddling and interfering rationality (yet again!), hence shun any learning?

Any such minor, within-season adaptations would remain those of a pure (not hybrid) risk-coping strategy: only the conservator makes the premium-setting decision, not the nurturing Adaptor who, in any case, is (theoretically) not directly a risk-coping type. Only the conservator (or the maximizer, manager, or pragmatist) has its hands on the steering wheel.

Salient for now closing this PostScript (and our article), however, is this. The given risk-coping rationality is experiencing merely what we may call a reactive learning. It is not, as we shall now see, deliberately wielding a metaphorical billiard cue while steering the company, to become thus pro-active in its learning.

THE ADAPTOR’S PROBING FUNCTION

There is a yet more advanced and sophisticated way of doing things in the toolkit of adaptive control engineering. It is called dual adaptive control. It obliges us to look back, to the Link between Parts I and II of our article, to recall the iconography of the ball on the surface. That iconography was introduced there in order to illuminate the differences between stability-instability contra resilience in a company’s performance.

Dual Adaptive Control: The Steering Wheel and The Billiard Cue

In dual adaptive control, the decisions u emanating from the controller K block combine two functions: of steering company affairs in the desired direction; and of probing the uncertainties about the system’s behavior (its O block) and those of its environment (the d). The makeups of both the “System” and the system’s surrounding “Environment” are therefore capable of being probed, in principle.

Algebraically, we have

u = uSteering + uProbing

in which the probing element of the action applied to the system is chosen to be prudently small in comparison with the steering element. Thus, as things move through time, the uProbing delivers consequences that inform and improve understanding of the way the structure of the system is evolving over time. It contributes, by design, to updating of the time-varying parameters (α(T)) in general, i.e., the parameters associated with all three domains of modeling: those of the disturbances d; company operations (O); and company decision strategy K.

We may align the wielding of the billiard cue with the probing component of dual adaptive control, and the driver’s hands on the steering wheel with (no surprise) the steering component. We may identify one of the basic four risk-coping strategies as the sole holder of the steering wheel and the special “+1” (fifth) rationality of the Adaptor as the sole holder of the probing cue. Having done so, let us pause to note something of significance: not only are we charging the Adaptor with responsibility for the switching and nurturing functions, but also here and now for a third function of probing, for the express purpose of deliberate, pro-active learning on behalf of the company.

By definition, therefore, dual adaptive control in a business is always a hybrid strategy, comprising the Adaptor with one or the other of the maximizer, manager, conservator, or pragmatist. It is hybrid because, unlike the nurturing function of the Adaptor illustrated above in conjunction with the conservator risk-coping strategy, something of what the Adaptor decides about is realised in the single (but dual purpose) decision u.

Wielding the Billiard Cue

Historically, this notion of dual adaptive control had already migrated out of the aerospace sector by the mid-1970s, to be taken up by systems ecologist Holling and colleagues. It took shape under the title of the 1979 book Adaptive Environmental Assessment and Management and was tantamount to the K-block of the system (an agency, institution, or company) probing the uncertainties in that system’s understanding of Nature, while yet seeking to husband its behavior (admittedly to the benefit, in no small measure, of Man).[9] Three decades later, and within the setting of plural rationality (Cultural Theory), a companion means of probing the uncertainties surrounding an understanding of the social-power dynamics of the affairs of Man emerged. It goes under the rubric of Adaptive Community Learning.[10]

But are there any distinct differences, we should enquire, in the manner in which the Adaptor might wield the billiard cue at different times and in different places? The direction and the power of the striking of the ball are two of the Adaptor’s degrees of freedom to probe. The ball-and-surface iconography serves well the purpose of illustration.

We have thus the four iconic shapes of the stability-instability surface at the heart of each rationality’s beliefs about the way the world is: the ꓴ of boom; the symbol-less bowl-with-rims-turned-down of moderate; the ∩ of bust; and the em-dash flatlands “—” of uncertain. This creates the possibility of four instances of the Adaptor’s probing function:

  • With the maximizer of boom at the steering wheel, and with the Adaptor in agreement that boom is the correct season of risk, the Adaptor might strike the ball with the cue as vigorously as it wishes, and in any direction. Company affairs would not escape the ꓴ bounds of the acceptable.
  • The probing might be more circumspect under the manager’s risk-coping in the season of moderate, with the Adaptor perhaps doing no more than tapping the ball in a carefully targeted direction, duly informed by expert actuarial judgement — certainly nothing wild.
  • Probing under the conservator’s stewardship would be inclined to explore not the nature of the way things are today, but to firm up (no matter by how little) which exactly of its myriad dreaded futures is the more “reachable”, the more likely to come to pass. After all (the conservator is convinced), a puff of wind this very moment in the here and now might topple the ball from its perch atop the ∩, to bring about disaster — never mind the merest ping of a billiard cue.[11]
  • Last, with the fourth basic rationality in the company driving seat, the Adaptor might readily concur with that pragmatist type: that the cue be taken out of active service, stowed safely in the cargo hold, and the hatches duly battened down tight.

There could, therefore, be four kinds of joint steering-probing strategies:

  • Maximizer-Adaptor, in which the Adaptor should be looking outwards and probing for today’s more (as opposed to less) profitable lines of new business “out there”.
  • Manager-Adaptor, with the latter deftly probing the company’s risk-adjusted returns for the one or two that marginally elevate the extent to which growth in those returns may out-perform the economy in general.
  • Conservator-Adaptor, wherein the Adaptor is scanning the range of the company’s business, for actual loss-making activities today and those potentially of tomorrow.
  • Pragmatist-Adaptor, in which the Adaptor is turning its senses inwards, towards eliminating any point of concentration of risk in the company’s lines of business, especially those with no scope for immediate escape from the commitment.

All of which could take us beyond even a “Vintage 2022” of the work of Benjamin and Balzer from the 1970s and 1980s (with which all this began). For imagine this. The premium-pricing decision of an insurer’s profit-sharing scheme is set so as not only to stabilize and steer company performance in a successful, desired direction, but also to probe deliberately the unknowns in the company’s risk environment — to render less unpredictable, for example, the pattern of claims submissions.

All of which, to be frank, may strike one as perhaps altogether “too clever by half”.

The Much-vaunted Re-engineering of Control is Not Unbounded

Achieving a “maximally” smooth and swift recovery of equilibrium — bounce back — is a classical goal of control engineering: that these desired features of the recovery under closed-loop control should be palpable improvements upon what would be the case under open-loop control. But such control (re-)engineering is bounded, in at least two very significant ways.

First, there are limits to the decisions that can be applied to the system, i.e., the u. Premium-prices and reserving amounts are bounded. They cannot be wound up or down without limit, even when the company is facing demands to do so, because of larger-than-planned-for Mismatches between what it wants (yw) and what it is getting (y).

Second, the shape-shifting choice of the structure and parameterization of the control rule (the decision strategy in the K block) may be bringing the thereby improved but stable closed-loop system to the brink of instability (the marvel of that Lockheed F117 Nighthawk jet) — but without the company knowing this. For simply put, there is uncertainty about both the system and the incoming disturbance stream d, neither of which (system or disturbance) may conform to what has been presumed in the design of the decision-making strategy.

The “Load Problem” Versus the “Regulator Problem” of Control Engineering

Risk-coping within a given season can be regarded as the problem of designing a controller for solving what is called the load problem in control engineering. The problem is specified thus:

Given a fixed set of wants (yw), design the strategy in the controller K block so as to “reject” all the deleterious effects of the incoming disturbances of the risk stream d, in order thereby to keep what the company gets (y) as close as possible to the yw at all times.

Flight in an aircraft illustrates this well: the smooth flight (y) at the chosen altitude (yw), regardless of the buffeting d (and indeed, the slow decline in aircraft mass).

Switching from one season of risk to another brings a new autopilot into the driving seat with wants yw for company performance that are different from the yw of the ousted auto-pilot. Continuing to keep actual company performance (y) as close as possible to the changing wants yw is referred to as the regulator (or servomechanism) problem:

Given a changing set of wants, technically a yw changing with time (t), design the strategy in the controller so as to transfer what the company is getting y(t) in a manner whereby the revised wants are continuously delivered as soon as possible, and without deviation.

Flight again illustrates the matter. The plane is to change from cruising at 30,000 ft to cruising at 35,000 ft. And we all know this can be expedited smoothly in a desirable manner.

What we might not notice is the fact of the aircraft exhibiting non-minimum-phase dynamic behavior. Once the decision to ascend (u) is issued, the center of mass of the aircraft (y) falls before rising to track the shift from the previous desired altitude (yw) to the new one. Even though the desire is to go up, things go down before they go up (and vice versa, in theory). It was this idea that we linked to the challenge of building resilience into the performance of an asset portfolio in Part II of our article.

To Close: Thinking Through the Changing “Wants” of the Business — Under RA for ERM

In RA for ERM, we have yet to think through the consequences of the control engineering solutions to the regulator problem in any detail (as for so much else in this “work in progress”). Nevertheless, we can sketch out some first implications of what the issue might look like — and then reflect (in the fullness of time, well beyond the scope of this article) on whether something useful might be done about it.

The nature of the wants (yw) of each of the four risk-coping types may be summarized crudely as follows:

  • The risk-trading maximizer wants to maximize company profits by maximizing growth in potentially profitable (possibly new) lines of business.
  • The risk-steering manager seeks to optimize the company’s risk-adjusted returns, to push them just that little bit further above the rate of growth in the economy as whole.
  • The loss-controlling conservator wants to minimize both the actual company losses of “today” and the potential losses “tomorrow”, while not neglecting the interest of some (if not all) of the company’s customer groups.
  • The diversifying pragmatist simply desires the survival of the company, by diluting out any concentration of risks and minimizing the illiquidity of the company’s financial commitments.

Given these four sets of wants, we can surmise that should the season of boom (maximizer) transition to that of moderate (manager), there may not be all that much of a regulator problem to be solved. The same might be true of any transition from bust (conservator) to uncertain (pragmatist) season. Perhaps both can be expedited sufficiently “smoothly”, simply as a result of the Adaptor throwing the switch.

Other possible transitions seem less straightforward. Perhaps they would call for some of the nurturing and probing of the Adaptor. But could a boom-to-bust transition ever be anything but a jolt with all the damaging ramifications of such a jolt? Even when the exceptional Adaptor is ever investing in the company’s capacity to navigate with aplomb through all and any of the chops and changes in the seasons of risk?

[1] The models do not have to be algebraic time-series models. Indeed, the prior research on which our current argument in this article is founded was conducted predominantly with reference to ordinary differential equations (see, for example, Beck and van Straten (1983) and Beck (2002)).

[2] In the following, when necessary for clarity, the three subscripts of d, O, and K will be used to distinguish among the three particular domains of (diagnostic) models to which the parameters α refer specifically.

[3] Such predictability of α(T) was not an issue in the case of a guided missile, because uppermost there was to have the best snapshot for the present moment, hence to determine the current action u(t). Besides, given that corrective action would again be shortly recomputed and applied, as u(t+1), the consequences of getting things wrong with u(t) would not propagate far before being rectified.

[4] Technically, there are some underlying, algorithmic challenges that our argument is necessarily glossing over, if, that is, any of our models were ever to be realised computationally in the practice of RA for ERM (and, as we have been at pains to point out, this is not our immediate purpose herein). In order to implement recursive estimation of the model’s parameters α, it may be necessary to make some critical prior assumptions about just how quickly or slowly the analyst believes these various model coefficients will change with time. The issue will be recognisable as that of having to specify how quickly to forget the past, hence be more or less “open” to learning in the future. It is something of a chicken-and-egg problem. A parameter (coefficient) presumed to change relatively quickly (slowly) may well end up being estimated as indeed changing relatively quickly (slowly). Many will be familiar with the device of exponential “forgetting” of past data. There are other ways around the issue, wherein a minimum of such prior assumptions have to be made. One such method entails using a so-called “innovations process” representation (Lin and Beck, 2012).

[5] Alternatives, not mentioned in our article or its Link, are available. Instead of the model being an econometric-like time-series model, it could be an implementation of Bayes’ rule, in which the prior, posterior, and conditional probabilities may be thought of as the parameters (β) — ones, in fact, varying with slow time T. But why use the symbol β for the transition probabilities? Because here we are needing to refer to parameters (β), which may vary with slow time T, that determine how the archetypal parameters of the decision rule in the K block (αK) are likely to change: from those of their current location in the αK space, at, say, the pole of αManager in the current season of moderate, to that of αPragmatist in anticipation — most probably (as a function of β(T)) — of the imminent season of uncertain. A significant part of our SoA Research Report deals with the identification of such transition probabilities from empirical time-series on annual sequences of insurer market and performance data.

[6] An expressly specific model structure is, in fact, treated in our (2021) SoA Research Report. It mirrors the most basic structure of a feedback controller in classical control engineering, referred to as a Proportional-Integral-Derivative action (or PID) control rule.

[7] The controlling actions emanating from the policy (the u(t)) will still be those of, for example, central bank interest-rate settings and adjustments. They will be being adjusted in quick time t, perhaps quarterly. The structure of the policy, however, will be changing over slow time T, over the years and decades.

[8] Thompson (2018).

[9] Holling (1979).

[10] Beck et al (2002, 2020) and Beck (2011).

[11] Note this, however. It is not just the conservator, with the ball atop the ∩, who might want to probe the attainability of a future niveau of company performance, either feared or hoped for. Adaptive Community Learning comes with a so-called Reachable Futures Analysis. It is discussed in our (2020) research report for the AFIR-ERM section of the IAA (Beck et al (2020).

REFERENCES

Beck, M B (Ed) (2002), “Environmental Foresight and Models: A Manifesto”, Elsevier, Oxford, 473pp.

Beck, M B (2011), “Cities as Forces for Good in the Environment: Sustainability in the Water Sector”, Warnell School of Forestry and Natural Resources, University of Georgia, Athens, Georgia, 2011, (ISBN: 978-1-61584-248-4), xx + 165pp (available on-line as http://cfgnet.org/archives/587).

Beck, M B, Ingram, D, and Thompson, M (2020), “Model Governance and Rational Adaptability in Enterprise Risk Management”, Final Project Report, AFIR-ERM Section, International Association of Actuaries (IAA-AAI), Metcalf, Ottawa, 88pp.

Beck, M B, and 13 co-authors (2002), “Developing a Concept of Adaptive Community Learning: Case Study of a Rapidly Urbanizing Watershed”, Integrated Assessment, 3(4), pp 299-307.

Beck, M B, and van Straten, G (Eds) (1983), “Uncertainty and Forecasting of Water Quality”, Springer, Berlin, 386pp.

Holling, C S (1977), “Myths of Ecology and Energy”, in Proceedings Conference (21-22 October, 1976) on Future Strategies for Energy Development (I Kiefer, ed), Oak Ridge Associated Universities, Oak Ridge, Tennessee, pp 34-39.

Lin, Z, and Beck, M B (2012), “Accounting for Structural Error and Uncertainty in a Model: An Approach Based on Model Parameters as Stochastic Processes”, Environmental Modelling & Software, 27-28, pp 97-111.

Thompson, M (2018), “How Banks and Other Financial Institutions Think”, British Actuarial Journal, 23, E5, pp 1-16 (doi:101017/S1357321717000253).

Underwood, A, Thompson, M, and Ingram, D (2013), “All on the Same Train, but Heading in Different Directions. Risk Attitudes Among Insurance Company Management and Implications for Forming a Risk Culture”, Essay, Chief Risk Officers (CRO) Competition.