Actuarial Science Seminar: Accounting for model uncertainty in optimal insurance contract design. An example of cyclone risk in Madagascar

Abstract: In stochastic optimization for extreme risk management, the optimal solution heavily depends on the chosen model for scenario generation. A common approach is to base the risk estimates on observed data and to use the statistically obtained estimates for finding the optimal risk management strategies. However, the fact that statistical estimates can never give precise values of the unknown parameters due to an estimation error, is quite often neglected. Moreover, the choice of the probability model, i.e., the class of possible distributions, is typically chosen by the statistician and is not further questioned. In reality though, statistical estimation procedures do not allow to single out one specific probability model, but only an entire set of models can be determined, in which the true model lies with a pre-specified probability. This confidence set can be taken as the set of models for a minimax decision, where the best decision under the worst model in the model set is sought for. In this talk, we will demonstrate how the model uncertainty can be incorporated into the decision-making process. We use a nonparametric approach for quantifying the model uncertainty and a minimax setup to find model-robust solutions. The method is used for the solution of a risk management problem involving the optimal design of an insurance contract for cyclone risks in Madagascar