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**Life-cycle planning with ambiguous economics and mortality risks.**
*(English)*
Zbl 1429.91283

Summary: 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.

### MSC:

91G05 | Actuarial mathematics |

91B06 | Decision theory |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

### Keywords:

life-cycle model; strategic planning; mortality risks; preretirement and postretirement phases
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\textit{Y. Shen} and \textit{J. Su}, N. Am. Actuar. J. 23, No. 4, 598--625 (2019; Zbl 1429.91283)

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### References:

[1] | Anderson, E. W.; Hansen, L. P.; Sargent., T. J., A quartet of semigroups for model specification, robustness, prices of risk, and model detection, Journal of the European Economic Association, 1, 1, 68-123 (2003) |

[2] | Bo, L.; Capponi., A., Robust optimization of credit portfolios, Mathematics of Operations Research, 42, 1, 30-56 (2017) · Zbl 1360.91147 |

[3] | Chen, A.; Hentschel, F.; Xu., X., Optimal retirement time under habit persistence: What makes individuals retire early?, Scandinavian Actuarial Journal, 2018, 3, 225-49 (2018) · Zbl 1396.91681 |

[4] | Dimmock, S. G.; Kouwenberg, R.; Mitchell, O. S.; Peijnenburg., K., Ambiguity aversion and household portfolio choice puzzles: Empirical evidence, Journal of Financial Economics, 119, 3, 559-77 (2016) |

[5] | Dybvig, P. H.; Liu., H., Lifetime consumption and investment: Retirement and constrained borrowing, Journal of Economic Theory, 145, 3, 885-907 (2010) · Zbl 1245.91044 |

[6] | Escobar, M.; Ferrando, S.; Rubtsov., A., Robust portfolio choice with derivative trading under stochastic volatility, Journal of Banking and Finance, 61, 142-57 (2015) |

[7] | Escobar, M.; Ferrando, S.; Rubtsov., A., Dynamic derivative strategies with stochastic interest rates and model uncertainty, Journal of Economic Dynamics and Control, 86, 49-71 (2018) · Zbl 1401.91516 |

[8] | Flor, C. R.; Larsen, L. S., Robust portfolio choice with stochastic interest rates, Annals of Finance, 10, 2, 243-65 (2014) · Zbl 1298.91137 |

[9] | FRB. 2016. Survey of consumer finances. Technical report, Federal Reserve Bank. |

[10] | Hansen, L. P.; Sargent., T. J., Seasonality and approximation errors in rational expectations models, Journal of Econometrics, 55, 1-2, 21-55 (1993) · Zbl 0755.62086 |

[11] | Hansen, L. P.; Sargent, T. J.; Wang., N. E., Robust permanent income and pricing with filtering, Macroeconomic Dynamics, 6, 1, 40-84 (2002) · Zbl 1001.91017 |

[12] | Hu, Y.; Imkeller, P.; Müller., M., Utility maximization in incomplete markets, Annals of Applied Probability, 15, 3, 1691-1712 (2005) · Zbl 1083.60048 |

[13] | Huang, H.; Milevsky., M. A., Portfolio choice and mortality-contingent claims: The general HARA case, Journal of Banking and Finance, 32, 11, 2444-52 (2008) |

[14] | Huang, H.; Milevsky, M. A.; Wang., J., Portfolio choice and life insurance: The CRRA case, Journal of Risk and Insurance, 75, 4, 847-872 (2008) |

[15] | Hugonnier, J.; Pelgrin, F.; St-Amour., P., Valuing life as an asset, as a statistic and at gunpoint (2018) |

[16] | Hurd, M. D.; Mcgarry., K., Evaluation of the subjective probabilities of survival in the health and retirement study, The Journal of Human Resources, 30, 268-92 (1995) |

[17] | Hurd, M. D.; Mcgarry., K., The predictive validity of subjective probabities of survival, Economic Journal, 112, 482, 966-985 (2002) |

[18] | Jian, X.; Yi, F.; Zhang., J., Investment and consumption problem in finite time with consumption constraint, ESAIM: Control, Optimisation and Calculus of Variations, 23, 4, 1601-15 (2017) · Zbl 1382.35347 |

[19] | J.P. Morgan. 2018. Long-term capital market assumption. Technical report, J.P. Morgan. |

[20] | Johansson, P.-O., On the value of changes in life expectancy, Journal of Health Economics, 15, 1, 105-13 (1996) |

[21] | Kraft, H.; Munk., C., Optimal housing, consumption, and investment decisions over the life-cycle, Management Science, 57, 6, 1025-41 (2011) · Zbl 1218.91049 |

[22] | Kraft, H.; Munk, C.; Wagner., S., Housing habits and their implications for life-cycle consumption and investment, Review of Finance, 22, 5, 1737-62 (2018) · Zbl 1425.91264 |

[23] | Lockwood, L. M., Bequest motives and the annuity puzzle, Review of Economic Dynamics, 15, 2, 226-43 (2012) |

[24] | Maenhout, P. J., Robust portfolio rules and asset pricing, The Review of Financial Studies, 17, 951-83 (2004) |

[25] | Maenhout, P. J., Robust portfolio rules and detection-error probabilities for a mean-reverting risk premium, Journal of Economic Theory, 128, 1, 136-63 (2006) · Zbl 1152.91535 |

[26] | Merton, R. C., Lifetime portfolio selection under uncertainty: The continuous-time case, The Review of Economics and Statistics, 51, 3, 247-257 (1969) |

[27] | Milevsky, M. A.; Young., V. R., Annuitization and asset allocation, Journal of Economic Dynamics and Control, 31, 9, 3138-177 (2007) · Zbl 1163.91440 |

[28] | Moore, K. S.; Young., V. R., Minimizing the probability of lifetime ruin when shocks might occur: Perturbation analysis, North American Actuarial Journal, 20, 1, 17-36 (2016) · Zbl 1414.91349 |

[29] | Munk, C.; Sørensen., C., Dynamic asset allocation with stochastic income and interest rates, Journal of Financial Economics, 96, 3, 433-62 (2010) |

[30] | Peijnenburg, K., Life-cycle asset allocation with ambiguity aversion and learning, Journal of Financial and Quantitative Analysis, 53, 5, 1963-94 (2018) |

[31] | Peijnenburg, K.; Nijman, T.; Werker., B. J., The annuity puzzle remains a puzzle, Journal of Economic Dynamics and Control, 70, 18-35 (2016) · Zbl 1401.91181 |

[32] | Pliska, S. R.; Ye., J., Optimal life insurance purchase and consumption/investment under uncertain lifetime, Journal of Banking and Finance, 31, 5, 1307-19 (2007) |

[33] | Ramsey, F. P., A mathematical theory of saving, The Economic Journal, 38, 152, 543-59 (1928) |

[34] | Richard, S. F., Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model, Journal of Financial Economics, 2, 2, 187-203 (1975) |

[35] | Rosen, S., The value of changes in life expectancy, Journal of Risk and Uncertainty, 1, 3, 285-304 (1988) |

[36] | Shen, Y.; Sherris., M., Lifetime asset allocation with idiosyncratic and systematic mortality risks, Scandinavian Actuarial Journal, 2018, 4, 294-327 (2018) · Zbl 1416.91221 |

[37] | Viceira, L. M., Optimal portfolio choice for long-horizon investors with nontradable labor income, Journal of Finance, 56, 2, 433-70 (2001) |

[38] | Wang, S., Premium calculation by transforming the layer premium density, ASTIN Bulletin, 26, 1, 71-92 (1996) |

[39] | Yaari, M. E., Uncertain lifetime, life insurance, and the theory of the consumer, The Review of Economic Studies, 32, 2, 137-50 (1965) |

[40] | Young, V. R.; Zhang., Y., Lifetime ruin under ambiguous hazard rate, Insurance: Mathematics and Economics, 70, 125-34 (2016) · Zbl 1371.91172 |

[41] | Zeng, X.; Wang, Y.; Carson., J. M., Dynamic portfolio choice with stochastic wage and life insurance, North American Actuarial Journal, 19, 4, 256-72 (2015) · Zbl 1414.91246 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.