Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty

Zhongfei Li, Ken Seng Tan and Hailiang Yang

North American Actuarial Journal, 2008, vol. 12, issue 1, 47-64

Abstract: In this article we investigate three related investment-consumption problems for a risk-averse investor: (1) an investment-only problem that involves utility from only terminal wealth, (2) an investment-consumption problem that involves utility from only consumption, and (3) an extended investment-consumption problem that involves utility from both consumption and terminal wealth. Although these problems have been studied quite extensively in continuous-time frameworks, we focus on discrete time. Our contributions are (1) to model these investmentconsumption problems using a discrete model that incorporates the environment risk and mortality risk, in addition to the market risk that is typically considered, and (2) to derive explicit expressions of the optimal investment-consumption strategies to these modeled problems. Furthermore, economic implications of our results are presented. It is reassuring that many of our findings are consistent with the well-known results from the continuous-time models, even though our models have the additional features of modeling the environment uncertainty and the uncertain exit time.

Date: 2008
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DOI: 10.1080/10920277.2008.10597499

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