On optimal proportional reinsurance and investment in a hidden Markov financial market

This paper investigates the optimal reinsurance and investment in a hidden Markov financial market consisting of non-risky (bond) and risky (stock) asset. We assume that only the price of the risky asset can be observed from the financial market. Suppose that the insurance company can adopt proportional reinsurance and investment in the hidden Markov financial market to reduce risk or increase profit. Our objective is to maximize the expected exponential utility of the terminal wealth of the surplus of the insurance company. By using the filtering theory, we establish the separation principle and reduce the problem to the complete information case. With the help of Girsanov change of measure and the dynamic programming approach, we characterize the value function as the unique solution of a linear parabolic partial differential equation and obtain the Feynman-Kac representation of the value function.