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Optimally investing to reach a bequest goal

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  • Bayraktar, Erhan
  • Young, Virginia R.

Abstract

We determine the optimal strategy for investing in a Black–Scholes market in order to maximize the probability that wealth at death meets a bequest goal b, a type of goal-seeking problem, as pioneered by Dubins and Savage (1965, 1976). The individual consumes at a constant rate c, so the level of wealth required for risklessly meeting consumption equals c/r, in which r is the rate of return of the riskless asset.

Suggested Citation

  • Bayraktar, Erhan & Young, Virginia R., 2016. "Optimally investing to reach a bequest goal," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 1-10.
    • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:1-10
    DOI: 10.1016/j.insmatheco.2016.05.015
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    References listed on IDEAS

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    1. Victor C. Pestien & William D. Sudderth, 1985. "Continuous-Time Red and Black: How to Control a Diffusion to a Goal," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 599-611, November.
    2. Sid Browne, 1999. "Beating a moving target: Optimal portfolio strategies for outperforming a stochastic benchmark," Finance and Stochastics, Springer, vol. 3(3), pages 275-294.
    3. William D. Sudderth & Ananda Weerasinghe, 1989. "Controlling a Process to a Goal in Finite Time," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 400-409, August.
    4. Erhan Bayraktar & Virginia Young, 2007. "Correspondence between lifetime minimum wealth and utility of consumption," Finance and Stochastics, Springer, vol. 11(2), pages 213-236, April.
    5. 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.
    6. Bayraktar, Erhan & Promislow, S. David & Young, Virginia R., 2014. "Purchasing life insurance to reach a bequest goal," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 204-216.
    7. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    8. 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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    Citations

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    Cited by:

    1. Kevin Maritato & Morton Lane & Matthew Murphy & Stan Uryasev, 2022. "Optimal Allocation of Retirement Portfolios," JRFM, MDPI, vol. 15(2), pages 1-17, February.
    2. Liang, Xiaoqing & Young, Virginia R., 2023. "Annuitizing at a bounded, absolutely continuous rate to minimize the probability of lifetime ruin," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 80-96.
    3. Angoshtari, Bahman & Bayraktar, Erhan & Young, Virginia R., 2015. "Minimizing the expected lifetime spent in drawdown under proportional consumption," Finance Research Letters, Elsevier, vol. 15(C), pages 106-114.
    4. Asaf Cohen & Virginia R. Young, 2015. "Minimizing Lifetime Poverty with a Penalty for Bankruptcy," Papers 1509.01694, arXiv.org.
    5. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2015. "Optimal Investment to Minimize the Probability of Drawdown," Papers 1506.00166, arXiv.org, revised Feb 2016.
    6. Christopher J. Rook, 2015. "Optimal Equity Glidepaths in Retirement," Papers 1506.08400, arXiv.org.
    7. Dongchen Li & Virginia R. Young, 2020. "Maximizing expected exponential utility of consumption with a constraint on expected time in poverty," Annals of Finance, Springer, vol. 16(1), pages 63-99, March.
    8. Fangyuan Dong & Nick Halen & Kristen Moore & Qinglai Zeng, 2019. "Efficient Retirement Portfolios: Using Life Insurance to Meet Income and Bequest Goals in Retirement," Risks, MDPI, vol. 7(1), pages 1-11, January.
    9. Landriault, David & Li, Bin & Li, Danping & Li, Dongchen, 2016. "A pair of optimal reinsurance–investment strategies in the two-sided exit framework," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 284-294.

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    More about this item

    Keywords

    Bequest motive; Consumption; Optimal investment; 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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