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Optimal investment strategy to minimize occupation time

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  • Erhan Bayraktar
  • Virginia Young

Abstract

We find the optimal investment strategy to minimize the expected time that an individual’s wealth stays below zero, the so-called occupation time. The individual consumes at a constant rate and invests in a Black-Scholes financial market consisting of one riskless and one risky asset, with the risky asset’s price process following a geometric Brownian motion. We also consider an extension of this problem by penalizing the occupation time for the degree to which wealth is negative. Copyright Springer Science+Business Media, LLC 2010

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  • Erhan Bayraktar & Virginia Young, 2010. "Optimal investment strategy to minimize occupation time," Annals of Operations Research, Springer, vol. 176(1), pages 389-408, April.
    • Handle: RePEc:spr:annopr:v:176:y:2010:i:1:p:389-408:10.1007/s10479-008-0467-2
    DOI: 10.1007/s10479-008-0467-2
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    References listed on IDEAS

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    1. Moshe A. Milevsky & Kristen S. Moore & Virginia R. Young, 2006. "Asset Allocation And Annuity‐Purchase Strategies To Minimize The Probability Of Financial Ruin," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 647-671, October.
    2. Kristen Moore & Virginia Young, 2006. "Optimal and Simple, Nearly Optimal Rules for Minimizing the Probability Of Financial Ruin in Retirement," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 145-161.
    3. 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.
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    Cited by:

    1. Lkabous, Mohamed Amine & Wang, Zijia, 2023. "On the area in the red of Lévy risk processes and related quantities," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 257-278.
    2. Kohatsu-Higa, A. & Makhlouf, A. & Ngo, H.L., 2014. "Approximations of non-smooth integral type functionals of one dimensional diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1881-1909.
    3. Cohen, Asaf & Young, Virginia R., 2016. "Minimizing lifetime poverty with a penalty for bankruptcy," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 156-167.
    4. 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.
    5. Iftikhar Ul Haq & Tanzeela Shaheen & Wajid Ali & Hamza Toor & Tapan Senapati & Francesco Pilla & Sarbast Moslem, 2023. "Novel Fermatean Fuzzy Aczel–Alsina Model for Investment Strategy Selection," Mathematics, MDPI, vol. 11(14), pages 1-23, July.
    6. Xiaoqing Liang & Virginia R. Young, 2020. "Minimizing the Probability of Lifetime Exponential Parisian Ruin," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 1036-1064, March.
    7. Asaf Cohen & Virginia R. Young, 2015. "Minimizing Lifetime Poverty with a Penalty for Bankruptcy," Papers 1509.01694, arXiv.org.
    8. Moawia Alghalith, 2012. "A New Stopping Time Model: A Solution to a Free-Boundary Problem," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 265-270, January.
    9. Erhan Bayraktar & Asaf Cohen, 2015. "Risk Sensitive Control of the Lifetime Ruin Problem," Papers 1503.05769, arXiv.org, revised Jul 2016.
    10. Alghalith, Moawia, 2013. "The interaction among production, hedging and investment decisions," Economic Modelling, Elsevier, vol. 30(C), pages 193-195.
    11. Zeddouk, Fadoua & Devolder, Pierre, 2022. "Pricing and hedging of longevity basis risk through securitization," LIDAM Discussion Papers ISBA 2022038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Moawia Alghalith, 2012. "New stochastic calculus," Papers 1211.5819, arXiv.org.
    13. Alghalith, Moawia, 2012. "Forward dynamic utility functions: A new model and new results," European Journal of Operational Research, Elsevier, vol. 223(3), pages 842-845.

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