Mean-variance Reinsurance-investment Strategy Selection Problem

ABSTRACT:We consider an optimal time-consistent reinsurance-investment selection problem for an insurer whose surplus is governed by a linear diffusion. In our model, the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a simplified financial market consisting of a risk-free asset and a risky asset.In this paper, we first consider that the dynamics of the risky asset are governed by a constant elasticity of variance (CEV) model to incorporate conditional heteroscedasticity as well as the feedback effect of an asset’s price on its volatility. The objective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Explicit forms for the optimal reinsurance-investment strategy and corresponding value function are obtained. Numerical examples are provided to illustrate how the optimal reinsurance-investment strategy changes when some model parameters vary. Finally, we study that the dynamics of the risky asset are governed by an Ornstein-Uhlenbeck (O-U) progress. Same as the previous procedure, explicit forms for the optimal time-consistent mean-variance investment strategy and corresponding value function are obtained.