Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (1): 306-320.

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Optimal Life Insurance, Consumption and Investment Problem in a Lévy Model

Xu Chen()   

  1. College of Mathematics and Statistics, Hunan Normal University, Changsha 410081
  • Received:2019-10-16 Online:2022-02-26 Published:2022-02-23
  • Supported by:
    the Key Projects of Hunan Provincial Department of Education(19A294)

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

CLC Number: 

  • O211.9
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