Expected exponential utility maximization of insurers with a Linear Gaussian stochastic factor model

In this paper, we consider the problem of optimal investment by an insurer. The wealth of the insurer is described by a Cramér–Lundberg process. The insurer invests in a market consisting of a bank account and m risky assets. The mean returns and volatilities of the risky assets depend linearly on economic factors that are formulated as the solutions of linear stochastic differential equations. Moreover, the insurer preferences are exponential. With this setting, a Hamilton–Jacobi–Bellman equation that is derived via a dynamic programming approach has an explicit solution found by solving the matrix Riccati equation. Hence, the optimal strategy can be constructed explicitly. Finally, we present some numerical results related to the value function and the ruin probability using the optimal strategy.