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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. 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.
    4. Erhan Bayraktar & Asaf Cohen, 2015. "Risk Sensitive Control of the Lifetime Ruin Problem," Papers 1503.05769, arXiv.org, revised Jul 2016.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Asaf Cohen & Virginia R. Young, 2015. "Minimizing Lifetime Poverty with a Penalty for Bankruptcy," Papers 1509.01694, arXiv.org.
    11. Alghalith, Moawia, 2013. "The interaction among production, hedging and investment decisions," Economic Modelling, Elsevier, vol. 30(C), pages 193-195.
    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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