  In this paper we study the optimal investment and reinsurance problem of an
insurance company whose investment preferences are described via a forward
dynamic exponential utility in a regime-switching market model. Financial and
actuarial frameworks are dependent since stock prices and insurance claims vary
according to a common factor given by a continuous time finite state Markov
chain. We construct the value function and we prove that it is a forward
dynamic utility. Then, we characterize the investment strategy and the optimal
proportional level of reinsurance. We also perform numerical experiments and
provide sensitivity analyses with respect to some model parameters.
