Optimal proportional reinsurance and dividend pay-out for insurance companies with switching reserves

Abstract

This paper presents a model for an insurance company that controls its risk and dividend payout. The financial reserve of this company is modeled as an Ito process with positive drift. 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 and risk exposure of this company depends on the dynamic state of the economy. Thus, in order to take into account the state of the economy, the drift process and the diffusion coefficient are modeled as a continuous time Markov chain. The aim is to maximize the dividend payout of this insurance company whose manager is risk averse. This problem is formulated as a Markovian optimal control problem, so the Hamilton-Jacobi-Bellman equation is solved to yield the solution.