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Portfolio Choice and Life Insurance: The CRRA Case

31 Pages Posted: 3 Mar 2006  

Moshe A. Milevsky

York University - Schulich School of Business

Huang Huaxiong

York University

Jin Wang

York University - Schulich School of Business

Multiple version iconThere are 2 versions of this paper

Date Written: December 2005

Abstract

We study a class of portfolio choice problems that combine life insurance and labor income under constant relative risk aversion preferences (CRRA) preferences for consumption, within the optimal control framework pioneered by Merton (1969, 1971). Our model differs from previous research by (i) focusing attention on the correlation between human capital and financial capital, and (ii) modeling the utility of the family as opposed to separating consumption and bequest. From a technical point of view we show how the underlying Hamilton-Jacobi-Bellman (HJB) equation can be simplified using a similarity reduction technique, which then allows for the implementation of an efficient numerical solution. And, for reasonable financial economic parameter values, a closed-form approximation is derived which greatly simplifies the numerical calculations. A variety of example illustrating our numerical algorithm are also provided. Our main qualitative result is that households whose primary breadwinner's wages are negatively correlated with financial market returns, should optimally purchase more life insurance and can afford to take more risky positions with their financial portfolio. In addition, we find that the optimal face value of life insurance is remarkably insensitive to the family's risk aversion.

Keywords: Asset Allocation, Retirement Planning, Life Cycle, Portfolio Choice

JEL Classification: D91, G11

Suggested Citation

Milevsky, Moshe A. and Huaxiong, Huang and Wang, Jin, Portfolio Choice and Life Insurance: The CRRA Case (December 2005). Available at SSRN: https://ssrn.com/abstract=887811 or http://dx.doi.org/10.2139/ssrn.887811

Moshe Arye Milevsky (Contact Author)

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

Huang Huaxiong

York University ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

Jin Wang

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

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