On optimal proportional reinsurance and investment in a partial Markovian regime-switching economy

In this paper, we consider the problem of optimal reinsurance and investment in a multiple risky assets market with appreciation rate driven by a hidden Markov chain. The surplus of the insurance company is modeled by a Brownian motion with drift and the objective function is the expected exponential utility. By using the filtering theory, we establish the separation principle and reduce the problem to the complete observed case. Through the dynamic programming approach and the Girsanov change of measure, we characterize the value function as the unique viscosity solution of a linear parabolic partial differential equation and obtain the Feynman-Kac representation of the value function.