Optimal control problem for hybrid pension plans under longevity risk for alpha-maxmin expected utility minimization

Abstract

This paper investigates the problem of portfolio selection and adjustment of hybrid pension plans under longevity risk. The longevity risk is described by a time-varying mortality rate, which is an extension of Markham’s law. Suppose that the financial market assets consist of a risk-free asset, a stock, and a defaultable bond. Specifically, the stock price is described by a constant elasticity of variance (CEV) model. The objective is to minimize interim adjustments to contributions and benefits under an exponential loss function, as well as the loss of terminal wealth. It is difficult for investors to fully understand the market information, so there is uncertainty in the financial market. By applying robust control theory to formulate investors’ aversion to uncertainty, we obtain the $\alpha$-robust optimal investment strategies and the adjustment strategies. Finally, numerical analysis is presented to discuss the influence of the model parameters on the $\alpha$-robust optimal control strategies.