Optimal proportional reinsurance and investment under partial information

In this paper, we study the optimal proportional reinsurance and investment strategy for an insurer that only has partial information at its disposal, under the criterion of maximizing the expected utility of the terminal wealth. We assume that the surplus of the insurer is governed by a jump diffusion process, and that reinsurance is used by the insurer to reduce risk. In addition, the insurer can invest in financial markets. We give a characterization for the optimal strategy within a non-Markovian setting. Malliavin calculus for Lévy processes is used for the analysis.