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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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    3. 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.
    4. Martin, Jessica & Villeneuve, Stéphane, 2021. "A Class of Explicit optimal contracts in the face of shutdown," TSE Working Papers 21-1183, Toulouse School of Economics (TSE), revised Apr 2022.
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    6. Jessica Martin & Stéphane Villeneuve, 2021. "A Class of Explicit optimal contracts in the face of shutdown," Working Papers hal-03124102, HAL.
    7. Joshua Aurand & Yu-Jui Huang, 2019. "Epstein-Zin Utility Maximization on a Random Horizon," Papers 1903.08782, arXiv.org, revised May 2023.
    8. Jessica Martin & Stéphane Villeneuve, 2023. "Risk-sharing and optimal contracts with large exogenous risks," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 1-43, June.
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    12. 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).

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