Combined Optimization of Portfolio and Risk Exposure of an Insurance Company

This paper presents a model for an insurance company that controls its risk and is allowed to invest in a financial market with just two assets a risk free asset and a stock. The financial reserve of this company is modelled as an Ito process with positive drift and constant diffusion coefficient. While the diffusion coefficient can be interpreted as the risk exposure, the drift can be understood as the potential profit. The new feature of this paper is to consider that the potential profit of this company depends on the dynamical state of the economy. Thus, in order to take into account the state of the economy, the drift process is modelled as a continuous time Markov chain. The aim is to maximize the reserve of an insurance company whose manager is risk averse. The optimal control problem is formulated and the Hamilton-Jacobi-Bellman equation is solved to yield the solution.