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Utility Maximization With Random Horizon: A Bsde Approach

Author

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  • MONIQUE JEANBLANC

    (Université d’Évry-Val-d’Essonne, LaMME UMR CNRS 8071, IBGBI, 23 Boulevard de France, 91037 Evry Cedex, France)

  • THIBAUT MASTROLIA

    (Université Paris Dauphine, CEREMADE UMR CNRS 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France)

  • DYLAN POSSAMAÏ

    (Université Paris Dauphine, CEREMADE UMR CNRS 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France)

  • ANTHONY RÉVEILLAC

    (INSA, Département GMM, IMT UMR CNRS 5219, Université de Toulouse, 135 Avenue de Rangueil, F-31077 Toulouse Cedex 4, France)

Abstract

In this paper, we study a utility maximization problem with random horizon and reduce it to the analysis of a specific backward stochastic differential equation (BSDE), which we call BSDE with singular coefficients, when the support of the default time is assumed to be bounded. We prove existence and uniqueness of the solution for the equation under interest. Our results are illustrated by numerical simulations.

Suggested Citation

  • Monique Jeanblanc & Thibaut Mastrolia & Dylan Possamaï & Anthony Réveillac, 2015. "Utility Maximization With Random Horizon: A Bsde Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-43, November.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:07:n:s0219024915500454
    DOI: 10.1142/S0219024915500454
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    References listed on IDEAS

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    Cited by:

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    4. Jessica Martin & St'ephane Villeneuve, 2021. "A Class of Explicit optimal contracts in the face of shutdown," Papers 2102.00001, arXiv.org.
    5. Huang, Zongyuan & Wang, Haiyang & Wu, Zhen, 2020. "A kind of optimal investment problem under inflation and uncertain time horizon," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    6. Alberto Gennaro & Thibaut Mastrolia, 2024. "Delegated portfolio management with random default," Papers 2410.13103, arXiv.org.
    7. Chong, Wing Fung, 2019. "Pricing and hedging equity-linked life insurance contracts beyond the classical paradigm: The principle of equivalent forward preferences," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 93-107.
    8. Joshua Aurand & Yu‐Jui Huang, 2023. "Epstein‐Zin utility maximization on a random horizon," Mathematical Finance, Wiley Blackwell, vol. 33(4), pages 1370-1411, October.
    9. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio and num\'eraire portfolio for market models stopped at a random time," Papers 1810.12762, arXiv.org, revised Aug 2020.
    10. Tahir Choulli & Sina Yansori, 2018. "Explicit description of all deflators for market models under random horizon with applications to NFLVR," Papers 1803.10128, arXiv.org, revised Feb 2021.
    11. Jessica Martin & Stéphane Villeneuve, 2021. "A Class of Explicit optimal contracts in the face of shutdown," Working Papers hal-03124102, HAL.
    12. Joshua Aurand & Yu-Jui Huang, 2019. "Epstein-Zin Utility Maximization on a Random Horizon," Papers 1903.08782, arXiv.org, revised May 2023.
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