Optimal (Re)Insurance Design: Ambiguity, Belief Heterogeneity, and Loss Aversion

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Financial crises have demonstrated the need for resilient financial and insurance markets. A key consideration in insurance markets is then the design of robust insurance contracts. Indeed, the theory of optimal insurance design is one of the cornerstones of actuarial science, and the question of what insurance contract is optimal from an insurance buyer's perspective lies at its core. A rigorous treatment of this question requires a mathematical formulation of an optimality criterion. The classical theory builds upon the foundations laid out by Arrow (1971) and is rooted in the classical model of choice under uncertainty, i.e. Expected-Utility Theory (EUT): an insurance seeker is a risk-averse EU-maximizing decision-maker (DM) facing an insurable loss represented by a random variable on a given probability space. In this case, classical Bayesian optimization methods can be used to show the optimality of a linear deductible contract. ******These foundational results have been extended in several directions while maintaining EUT's assumption that individuals are fully rational and know precisely the likelihoods associated with any decision-making situation. However, there is substantial empirical evidence that DMs are not rational in the sense of EUT and that the classical insurance model is too limiting. For instance, there are situations of ambiguity (model uncertainty) in which DMs are not able to fully assess the probabilistic environment involved, as well as situations where DMs differ from insurers in their assessment of likelihoods. Insurance of emerging risks is a prime example.******It is critically important to construct more realistic models of DM behaviour in problems of optimal insurance design so as to align theoretical predictions with reality, suitably inform policy-making and insurance market regulation, and guide actuarial practice and efficient contract design. This is the long-term goal of the research program proposed herein, and a core component of my previous research has focused on advancing this effort. The proposed research program will continue on this path by building upon my previous work and incorporating belief heterogeneity, ambiguity aversion, and loss aversion in optimal insurance design. ******On a technical level, this research will present serious mathematical challenges arising from the inapplicability of Bayesian optimization and/or classical measure-theoretic methods in a setting of ambiguity and/or loss aversion. The optimal insurance design problems will be formulated as non-convex optimization problems involving non-additive probability measures and Choquet integration. Novel techniques are needed based on non-additive measure theory, and the research proposed herein will leverage my previous work to accomplish this. Student training will be embedded in this research program at every stage, as exhaustively described in my research proposal.