Optimal investment and reinsurance for an insurer under Markov-modulated financial market

作者：Xu, Lin^*; Zhang, Liming; Yao, Dingjun

来源：Insurance: Mathematics and Economics , 2017, 74: 7-19.

DOI：10.1016/j.insmatheco.2017.02.005

• Optimal investment
• Reinsurance
• Markov modulated risk model
• HJB equation
• Ruin probability

This study examines optimal investment and reinsurance policies for an insurer with the classical surplus process. It assumes that the financial market is driven by a drifted Brownian motion with coefficients modulated by an external Markov process specified by the solution to a stochastic differential equation. The goal of the insurer is to maximize the expected terminal utility. This paper derives the Hamilton-Jacobi-Bellman (HJB) equation associated with the control problem using a dynamic programming method. When the insurer admits an exponential utility function, we prove that there exists a unique and smooth solution to the HJB equation. We derive the explicit optimal investment policy by solving the HJB equation. We can also find that the optimal reinsurance policy optimizes a deterministic function. We also obtain the upper bound for ruin probability in finite time for the insurer when the insurer adopts optimal policies.

• 单位
  安徽师范大学; 南京财经大学