Uncertainty Management: From Computation to Imagination

Understanding the difference between radical uncertainty versus risk BRYON ROBIDOUX

The world becomes more complex as time progresses, and uncertainty is everywhere. I have struggled and toiled over how to reduce the complexity of insurance and how organizations can tame uncertainty. As actuaries, we tend to use risk and uncertainty interchangeably, but they are quite different. We must understand the differences between them because I believe this oversight is tripping us up. It is, in my view, unnecessarily adding to regulatory and operational complexity—which could inevitably price customers out of our products.

Risk vs. Uncertainty

Recognizing that risk and uncertainty have very different properties means approaching uncertainty differently. Uncertainty belongs in two categories:1

  1. Resolvable is for processes that do not change with time, i.e., stationary, with well-defined event spaces and well-defined events, which happen frequently enough to capture the statistics of the process. It is equivalent to risk.
  2. Radical is everything else but can be further broken into:
    1. Epistemic uncertainty implies you lack knowledge, but the information is knowable.
    2. Aleatory uncertainty involves not knowing because an event is random and unpredictable, so it can only be known after it happens.

This distinction between resolvable and radical uncertainty becomes increasingly important as our business has moved from mainly risky mortality to significantly more radically uncertain market guarantees. This product mix change lies at the heart of our operational complexity. With radical uncertainty, you may not possess the relevant information until after the event occurs—if at all—thwarting optimization. Therefore, uncertainty cannot be a one-size-fits-all approach of treating everything as risk.2

Unlike the solar system, no universal principles mandate that human behavior stays fixed. Therefore, business, finance and regulation are constantly evolving.3 For example, the collateralized debt obligations (CDOs) that crippled the world during the 2007–2008 global financial crisis were based on a formula that related a CDO’s value to relatively stationary mortality processes. The introduction of the Commodities Futures Modernization and Gramm-Leach-Bliley legislative acts significantly changed the underlying processes governing mortgage defaults, tremendously violating the stationary process assumptions in the CDO formula.4

Here’s a look at three types of uncertainty:

  1. Resolvable uncertainty, which can use traditional methods of handling risk because they are synonymous.
  2. Epistemic uncertainty, which requires embracing new, nonlinear models based on complex systems and systems science,5 much like what weather forecasters began doing in the 1960s.6
  3. Aleatory uncertainty, which mandates being comfortable admitting things we cannot know.7 We must use our superpowers of reason and run through kill-the-company exercises, which are drills that create scenarios by imagining alternative outcomes that lead to potential vulnerabilities and opportunities in order to improve decision-making.

Rethinking epistemic models

According to Economyths, we need to move on to post-Pythagorean economics.

Pythagorean economics assumes a stable, optimal, linear, rational, mechanical system that is highly tuned and occasionally breaks for no apparent reason. The post-Pythagorean viewpoint sees the economy as a dynamic, organic system that is lively and in which change is the norm. Furthermore, probabilistic risk models based on efficiency, stability and traditional hedging instruments that attempt to remove risk should be replaced. Their replacements should be more straightforward and transparent, where risk cannot be precisely calculated and engineered away. These new models should incorporate complexity economics, network theory, nonlinear dynamics, evolutionary economics, fractal/extreme statistics and behavioral economics.8

Our superpowers to address aleatory uncertainty

A criticism of economics and behavioral economics is that they deem human cognition and reasoning as inferior design relative to computers; our biases and judgments are somehow flawed. However, we are part of 4.5 billion years of evolution, and our cognition is optimized for a radically uncertain world.9 In most cases where a company goes belly up or the economy tanks, the reasons are due to phenomena outside the models or different than those that were anticipated. Therefore, we need to use our deductive, inductive and abductive reasoning superpowers to imagine weaknesses in our models.

  • Deductive reasoning reaches logical conclusions from stated premises.
  • Inductive reasoning seeks to generalize from observations that may be supported or refuted by subsequent experience.
  • Abductive reasoning seeks to provide the best explanation of a unique event.10

Now that we understand there is an important distinction between risk and radical uncertainty, it is essential to know where the confusion came from.

Why the Confusion?

In the early 1960s, there was a debate between Milton Friedman and John Maynard Keynes over the use of subjective (Bayesian) probabilities for radical uncertainty. Subjective probabilities are based on beliefs of the events occurring. Keynes staunchly opposed them, and Friedman defended their use. Ultimately, Friedman was victorious. Friedman realized that subject probabilities allowed for efficiency and optimization by circumventing issues that radical uncertainty posed for objective (frequentist) probabilities. After this debate, the distinction between risk and uncertainty was seen as something other than essential and lay dormant.11

In recent years, there has been a resurgence of this debate, especially in the area of behavioral economics, because, in a radically uncertain world, people do not optimize; they cope. They find the best solution that will work for them at the moment. Aleatory and epistemic uncertainty makes enumerating all the events and their probabilities extremely unlikely. This fact thwarts efficiency and optimization. Sadly, this was in line with Keynes’s argument.12 The desire to insist on optimizing led us astray because it has us frame all uncertainty as risk.


Assuming that risks and uncertainty are the same was very convenient because it gave license to optimize all risks for the best outcome. This simplification impacts insurance regulation and accounting because it gives the impression that projecting more complicated and frequent calculations provides more information and security to the industry.

Ironically, I believe this convenient simplifying assumption adds a lot of expense and complexity to insurance operations. Our models are still running on the stationary chassis of the 2007–2008 crisis that brought the house of cards down! The stationary chassis is a direct result of treating all uncertainty as risk.

I believe our biggest problem lies in that we want to know what we cannot know. We want to give guarantees and comfort where they are not possible. If we have more scenarios, assumptions, data, controls, complex models, more this, more that, and more whatever, we can finally get the certainty, robustness and management we desire. This desire for certainty is human nature, but we must let it go because it is nearly impossible in radically uncertain situations.


Where does this leave us if we accept the idea that risk and radical uncertainty are different? Separating risk from uncertainty changes nothing, and it changes everything! It changes nothing because we still have large, complicated businesses that we must manage. We still have policyholders, regulators and other stakeholders who depend on us. We still have promises that we sold and must keep until maturity.

It changes everything because now we must divide uncertainty into three buckets:

  1. Resolvable
  2. Epistemic
  3. Aleatory

We have tons of data, technology and mathematics that our risk managers use to tame resolvable uncertainty. But the set of phenomena that fit into this bucket has shrunk. It is the radical uncertainty that requires innovation and new practices. In general, as uncertainty increases from resolvable to aleatory, we must migrate from computation to imagination. We can derive the correct solutions to tackle future challenges only when we truly understand uncertainty and its sources.

Bryon Robidoux, FSA, CERA, MAAA, is a consulting actuary at Milliman in Chesterfield, Missouri.

Statements of fact and opinions expressed herein are those of the individual authors and are not necessarily those of the Society of Actuaries or the respective authors’ employers.

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