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Lifetime ruin under ambiguous hazard rate

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  • Young, Virginia R.
  • Zhang, Yuchong

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 her hazard rate of mortality is ambiguous. 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.

Suggested Citation

  • Young, Virginia R. & Zhang, Yuchong, 2016. "Lifetime ruin under ambiguous hazard rate," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 125-134.
    • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:125-134
    DOI: 10.1016/j.insmatheco.2016.06.007
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    References listed on IDEAS

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    1. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
    2. Virginia Young, 2004. "Optimal Investment Strategy to Minimize the Probability of Lifetime Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(4), pages 106-126.
    3. Moshe Milevsky & Chris Robinson, 2000. "Self-Annuitization and Ruin in Retirement," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 112-124.
    4. Sid Browne, 1997. "Survival and Growth with a Liability: Optimal Portfolio Strategies in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 468-493, May.
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    Cited by:

    1. Junbeom Lee & Xiang Yu & Chao Zhou, 2019. "Lifetime Ruin under High-watermark Fees and Drift Uncertainty," Papers 1909.01121, arXiv.org, revised Oct 2020.
    2. Young, Virginia R., 2017. "Purchasing casualty insurance to avoid lifetime ruin," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 133-142.
    3. Li, Danping & Young, Virginia R., 2019. "Optimal reinsurance to minimize the discounted probability of ruin under ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 143-152.

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    More about this item

    Keywords

    Probability of lifetime ruin; Ambiguity aversion; Hazard rate uncertainty; Optimal control; Stochastic control;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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