Optimal Investment and Proportional Reinsurance in a Markov Modulated Market Model under Forward Preferences

In this work we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a dynamic forward utility of exponential type. We consider a combined financial/actuarial market model which is subject to different regimes modulated by a Markov process and where the insurance and the financial sides are mutually dependent. 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 reinsurance. We also present numerical experiments and provide sensitivity analysis with respect to the parameters of the model.