Life-Cycle Planning with Ambiguous Economics and Mortality Risks

Abstract

In this article, we study the strategic planning problem for a wage earner in a life-cycle model with stochastic lifetime. The wage earner aims to decide on the optimal portfolio choice, consumption, and insurance buying rules over the preretirement and postretirement phases. In addition, the wage earner is concerned about the uncertainty of economic and mortality models. In order to address the concern, the wage earner considers the optimal decisions under the worst-case scenario selected from a set of plausible alternative models. We find that the economic ambiguity and mortality ambiguity have substantially different impacts on the optimal decisions. Specifically, though the worst-case economic scenario depends only on the economic environment, the design of the worst-case mortality scenario is determined by the intricate interplays between the wage earner’s personal profile (e.g., health status, income dynamics, risk aversion, etc.) and the evolution of the economic environment. Moreover, the study of mortality ambiguity is also closely related to the value of statistical life, which can be positive and negative in general. Such a complicated theoretical structure underlying the study of mortality ambiguity can sometimes even overturn the direction of its impacts on the optimal decisions. Our article highlights the importance as well as the complexity for modeling ambiguity aversion in optimal planning studies, which desire more serious and critical treatments from the community of actuarial professionals.

ACKNOWLEDGEMENTS

The authors are indebted to three anonymous referees for their very thorough reading of the article, and the many constructive suggestions that resulted in an improved version.

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Additional information

Funding

The authors gratefully acknowledge the support of their research by the Society of Actuaries (SOA). Shen also acknowledges the support of his research by the Natural Sciences and Engineering Research Council (NSERC) of Canada.