Lifetime Ruin Under Ambiguous Hazard Rate

20 Pages Posted: 13 Jun 2015 Last revised: 30 Jun 2019

See all articles by V.R. Young

V.R. Young

University of Michigan at Ann Arbor - Department of Mathematics

Yuchong Zhang

University of Toronto - Department of Statistics

Date Written: June 11, 2015

Abstract

We determine the optimal robust investment strategy of an individual who targets a given rate of consumption and who seeks to minimize the probability of lifetime ruin when she does not have perfect confidence in her hazard rate of mortality. By using stochastic control, we characterize the value function as the unique classical solution of an associated Hamilton-Jacobi-Bellman equation, obtain feedback forms for the optimal strategies for investing in the risky asset and distorting the hazard rate, and determine their dependence on various model parameters. We also include numerical examples to illustrate our results, as well as perturbation analysis for small values of the parameter that measures one’s level of ambiguity aversion.

Keywords: probability of lifetime ruin, ambiguity aversion, hazard rate uncertainty, optimal control, stochastic control

JEL Classification: C61, G02, G11

Suggested Citation

Young, Virginia R. and Zhang, Yuchong, Lifetime Ruin Under Ambiguous Hazard Rate (June 11, 2015). Insurance: Mathematics and Economics, Vol. 70, 2016, Available at SSRN: https://ssrn.com/abstract=2617350 or http://dx.doi.org/10.2139/ssrn.2617350

Virginia R. Young (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States
734-764-7227 (Phone)

Yuchong Zhang

University of Toronto - Department of Statistics ( email )

700 University Ave.
Toronto, Ontario M5S 1Z5
Canada

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