Abstract
This paper developed a wealth allocation framework for longevity risk protection under stochastic lifetime. By combining the dynamics of wealth evolution and health evolution in stochastic multi-period discrete-time models, an optimization problem was formulated with the objective of maximizing lifetime utility of consumption and bequest. We implemented the framework in different scenarios and provided results to illustrate the practical implications of the framework. Computational results suggested that it is optimal for most people to purchase an annuity at some point in their lives. However, an individual’s health status, risk aversion, retirement objective, and the insurance charge associated with annuities could significantly influence the choice of optimal annuitization time, consumption plans, and trade off between lifetime versus fixed-term annuity.
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Notes
Research in behavioral science has shown that people tend to have a nonlinear and asymmetric perception of uncertainty, and hence weight the utility of each possible outcome with a transformed weight in some decision problems (Tversky and Shafir 1992).
By using a combination of multiple one-year-period branches, the size of the optimization problem can be substantially reduced at the cost of computational accuracy. Gupta and Li (2007) used this method and verified that a 4-year periods tree does not affect the accuracy too much.
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Acknowledgments
We are very grateful to the anonymous referees and to the editor, Professor Elizabeth M. Dolan, for their efforts and valuable comments which improved the previous versions of this paper. Li acknowledges financial support from the National Natural Science Foundation of China (71271214 and 70801063). All remaining errors are ours only.
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Gupta, A., Li, Z. Optimal Annuity Purchase Decisions Under Uncertain Lifetime. J Fam Econ Iss 34, 447–459 (2013). https://doi.org/10.1007/s10834-012-9340-1
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DOI: https://doi.org/10.1007/s10834-012-9340-1