MULTIPERIOD OPTIMAL INVESTMENTCONSUMPTION STRATEGIES WITH MORTALITY RISK AND ENVIRONMENT UNCERTAINTY

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.