Actuarial Science Seminar: Two Special Techniques in Optimal Control with Applications in Insurance

Abstract: In this talk I will introduce two special techniques to solve stochastic control problems in insurance. In the first part, we apply a perturbation approach to study an optimal dividend problem for an insurer who controls her investment, reinsurance (liability ratio) and dividend rates. The essential idea is to first solve such a problem over all constant strategies and then argue via perturbation that the optimal constant strategy remains optimal over all admissible strategies. In the second part, we consider an optimal investment and risk control problem for an insurer under the mean-variance (MV) criterion. The novelty is to provide an alternative time-consistent formulation for the original MV problem by introducing a deterministic auxiliary process that is defined forward in time. Our alternative formulation is different from the standard game-theoretical framework. For both parts, we obtain the value function and optimal strategies in closed-form and conduct economic analysis of the results. Joint works with Zhuo Jin, Zuo Quan Xu and Yang Shen.
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