Consumption and Non-Life Insurance Demand With Ambiguous Mortality

International Journal of Humanities and Social Science

© 2021 by SSRG - IJHSS Journal

Volume 8 Issue 6

Year of Publication : 2021

Authors : Ming Zhou, Xuejiao Chen, Bing Liu

10.14445/23942703/IJHSS-V8I6P103

How to Cite?

Ming Zhou, Xuejiao Chen, Bing Liu, "Consumption and Non-Life Insurance Demand With Ambiguous Mortality," SSRG International Journal of Humanities and Social Science, vol. 8,  no. 6, pp. 13-22, 2021. Crossref, https://doi.org/10.14445/23942703/IJHSS-V8I6P103

Abstract:

This study considers the optimal consumption and non-life insurance demand for an individual who concerns about the ambiguous hazard rate of her/his lifetime. We formulate the ambiguity of the mortality in terms of Girsanov's probability measure changing by which the hazard rate changes with respect to the equivalent measures. For two cases without and with the consideration of the ambiguity aversion in the mortality, we respectively obtain the closed-form solutions for the value function, the robust consumption policy, and non-life insurance demand for the individual by using the technique of dynamic programming principle. Our findings can be concluded as follows. The ambiguity about the lifetime does not affect the non-life insurance demand policy because of independence between mortality risk and wealth risk. The insurance demand is increasing with respect to risk-free interest rate, the individual's wealth, age, and the maximum wealth loss, but decreasing with respect to the frequency of the wealth loss and the price of insurance. As for consumption, the individual saves more and consumes less at youth, and consumption is increasing between middle age and retirement, which is completely consistent with the people's behavior. The price of insurance has little impact on consumption, while the ambiguity about life has a significant impact on consumption. The more uncertain the reference model, the more the individual would like to consume.

Keywords:

ambiguous hazard rate; Robust consumption policy; HJB-equation; insurance demand

References:

[1] Bayraktar, E., Zhang, Y., Minimizing the probability of lifetime ruin under ambiguity aversion. SIAM Journal on Control and Optimization, 53(1) (2015) 58--90.
[2] Fleming, W.H., Soner, M.,  Controlled Markov Processes and Viscosity Solutions: 2nd edition, Springer, New York (2006). 
[3] Liu, B., Zhou, M.,  Robust portfolio selection for individuals: minimizing the probability of lifetime ruin. Journal of Industrial and Management Optimization, 17 (2)  (2021) 937--952.
[4] Maenhout, P.J.,  Robust portfolio rules and asset pricing. Review of Financial Studies, 17 (4) (2004) 951--983.
[5] Merton, R.C., Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3(4) (1971) 373--413.
[6] Pliska, S.R., Ye, J.C., 2007. Optimal life insurance purchase and consumption/investment under uncertain lifetime. Journal of Banking and Finance, 31(5) (2007) 1307--1319.
[7] 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) (1975) 187--203.
[8] Uppal, R., Wang, T.,  Model misspecification and under diversification. The Journal of Finance, 58(6) (2003) 2465--2486.
[9] Yaari, M.E., 1965. Uncertain lifetime, life insurance, and the theory of the consumer. Review of Economic Studies, 32  (1965) 137--150.
[10] Young, V.R.,  Optimal investment strategy to minimize the probability of lifetime ruin. North American Actuarial Journal, 8(4) (2004)  105--126.
[11] Young, V.R., Zhang, Y.,  Lifetime ruin under ambiguous hazard rate. Insurance: Mathematics and Economics, 70 (2016) 125--134.