An Optimal Life Insurance Policy in the Continuous-Time Investment-Consumption Problem

Hideki Iwaki, Yusuke Osaki

Faculty of Business Administration, Kyoto Sangyo University, Kyoto, Japan.
Faculty of Economics, Osaka Sangyo University, Osaka, Japan.

DOI: 10.4236/jmf.2013.32029                

Abstract

This paper considers an optimal life insurance for a household subject to mortality risk. The household receives wage income continuously, which could be terminated by unexpected premature loss of earning power. In order to hedge the risk of losing income stream, the household enters a life insurance contract. The household may also invest their wealth into a financial market. Therefore, the problem is to determine an optimal insurance/investment/consumption strategy. To reflect a real-life situation better, we consider an incomplete market where the household cannot trade insurance contracts continuously. We provide explicit solutions in a fairly general setup.

Keywords

Life Insurance; Investment/Consumption Model; Martingale; Convex Duality

Conflicts of Interest

The authors declare no conflicts of interest.

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