Zachary Van Oosten
PhD Candidate, University of Waterloo
Room: M3 3127
The aggregate-then-evaluate approach to ambiguity
In this talk, we will discuss a new framework for incorporating ambiguity into decision-making under uncertainty. To develop a mathematical formalism for decision-making, one usually studies functionals on the space of random variables, where the interpretation of the functional depends on the problem's context. For example, functionals can be used to calculate capital requirements in quantitative risk management (risk measures) or to calculate premiums for insurable losses in actuarial science (premium principles). In practice, one usually begins by estimating a probabilistic model and using law-invariant functionals. This approach is convenient because calculating law-invariant functionals is tractable and leverages the extensive literature on statistical model building.
However, there is often considerable uncertainty or ambiguity about the probabilistic model estimated from the data. To address this, one often resorts to distributionally robust optimization. This is done by fixing a collection of competing probabilistic models and computing the worst-case value of the law-invariant functional under them. As we will discuss, distributionally robust optimization can be seen as an evaluate-then-aggregate (ETA) approach to ambiguity. This will then motivate us to discuss an aggregate-then-evaluate (ATE) approach. After defining this approach, we will discuss ways to ensure that decisions made through it respect normatively appealing properties, e.g., the preference for diversification.