Portfolio Choice and Life Insurance: The CRRA Case
31 Pages Posted: 3 Mar 2006
Date Written: December 2005
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: Suggested Citation