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Utility Maximization With Random Horizon: A Bsde Approach

Author

Listed:
  • 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

    as
    1. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Jeanblanc, Monique & Martellini, Lionel, 2008. "Optimal investment decisions when time-horizon is uncertain," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1100-1113, December.
    2. Bender, Christian & Denk, Robert, 2007. "A forward scheme for backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1793-1812, December.
    3. repec:dau:papers:123456789/9697 is not listed on IDEAS
    4. Vicky Henderson & Gechun Liang, 2014. "Pseudo linear pricing rule for utility indifference valuation," Finance and Stochastics, Springer, vol. 18(3), pages 593-615, July.
    5. repec:dau:papers:123456789/1803 is not listed on IDEAS
    6. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    7. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    8. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71.
    9. Bruno Bouchard & Huyên Pham, 2004. "Wealth-path dependent utility maximization in incomplete markets," Finance and Stochastics, Springer, vol. 8(4), pages 579-603, November.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Tahir Choulli & Sina Yansori, 2018. "Deflators and log-optimal portfolios under random horizon: Explicit description and optimization," Papers 1803.10128, arXiv.org.

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