Stochastic optimal control problems in risk management

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Stochastic control theory arises from decision-making problems under uncertainty; it studies how to optimize stochastic dynamical systems according to some predetermined performance criterion. Based on Bellman's principle of optimality, standard stochastic control problems in the (continuous-time) Markovian framework can be solved by following the dynamic programming principle, which leads to the Hamilton-Jacobi-Bellman equations. As an elegant and powerful technique, stochastic control has found numerous applications in economics, finance, insurance, and risk management. Recent development in these areas have brought many new challenges and opportunities to researchers to develop new methodologies for theoretical studies and numerical computation. The primary objective of this proposed research is to study some crucial problems in insurance and economics by utilizing stochastic control theory as the main technique. Specifically, we will consider (1) Annuitization puzzle; (2) Adverse selection and advantage selection in insurance markets; (3) Optimal fee structures of variable annuities; (4) Extreme risk mitigation; (5) Equilibrium pricing of general insurance. It is anticipated that this proposed research can improve risk management and provide key insights to practitioners and academic researchers. A significant number of papers are expected to be published in leading journals of related fields over the course of this research grant. Undergraduate students, graduate students, and postdoctoral fellows will be intensively involved and trained in this proposed research program.