关键词: 最优寿险消费投资, Lévy过程, 最小最大鞅测度

Abstract:

In this paper, we employ the Minimax martingale measure to investigate an optimal life insurance-consumption-investment problem faced by a wage-eaener with an uncertain lifetime. The financial market is comprised of one risk-free security and a risky security whose price is determined by an exponential Lévy process. The object of the wage-eaener is to maximize the expected utility. Based on the Minimax martingale measure, the explicit solutions for various utility functions are obtained. Furthermore, a numerical example is considered, and numerical simulations are presented to illustrate the effect of the parameters on the optimal strategies.

Key words: Optimal life insurance-consumption-investment, Lévy process, Minimax martingale measure