Actuaries love dealing with risk. Actuaries hate dealing with uncertainty. Their tool kit of creating well structured problems with defined probability distributions and parameters falls apart when dealing with uncertainty.
Barry Ritholtz had a good discussion on this distinction in 2012 regardin the stock market and political risk:
When we don’t know what any future outcome will be, but we understand the probability distribution — think of dice or a multiple choice exam — we have risk, but we do NOT have uncertainty. We never know what the roll of the dice will be, but we do know its one of six choices.
Is that uncertainty? The answer is of course not — it is an unknown outcome with well-defined possibilities. We may not know precisely which outcome will occur in advance, but we do know its either 1, 2,3, 4, 5 or 6. Call that risk….
Consider alternatively what is the true definition of Uncertainty: That occurs when we have no idea of what the possible outcome might be. The probability distribution is unknown (or so extremely large as to functionally be the same as unknown).
Let’s bring this out to an absurdly fun example. Next summer, I will be taking my kids to the North Carolina beach several times. If I give an actuary the name of the beach, the weekend that I will be there and whether or not my kids have any open bleeding scabs, that actuary can create a model. That model will rely on known data of shark migration patterns given the time of year, it will rely on a species distribution, it will rely on a deep data set of the past. The actuary will run that model a couple of thousand times through a Monte Carlo program and spit out a probability distribution that my kids will get bitten by a shark. If I pay the actuary a bit more, I’ll get an expected cost of insuring my kids against shark bites.
This is risk management. There is known data with identifiable distributions. The estimate will always have a bit of fuzz to it but the estimate will be close.
Now let’s replace this scenario. If I give an actuary a map of an unknown location where the only useful information on it is “There be monsters” the actuary will have a nervious breakdown if I ask them to give me a model of monster attacks. That is a model of extreme uncertainty as the data provides no guidance.
So let’s keep this in mind when we think of risk (sharks) and uncertainty (monsters).