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Wealth-path dependent utility maximization in incomplete markets

Author

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  • Bruno Bouchard

    ()

  • Huyên Pham

    ()

Abstract

Motivated by an optimal investment problem under time horizon uncertainty and when default may occur, we study a general structure for an incomplete semimartingale model extending the classical terminal wealth utility maximization problem. This modelling leads to the formulation of a wealth-path dependent utility maximization problem. Our main result is an extension of the well-known dual formulation to this context. In contrast with the usual duality approach, we work directly on the primal problem. Sufficient conditions for characterizing the optimal solution are also provided in the case of complete markets, and are illustrated by examples. Copyright Springer-Verlag Berlin/Heidelberg 2004

Suggested Citation

  • Bruno Bouchard & Huyên Pham, 2004. "Wealth-path dependent utility maximization in incomplete markets," Finance and Stochastics, Springer, vol. 8(4), pages 579-603, November.
  • Handle: RePEc:spr:finsto:v:8:y:2004:i:4:p:579-603
    DOI: 10.1007/s00780-004-0125-8
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    Citations

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    Cited by:

    1. Xiang Yu, 2011. "Utility maximization with addictive consumption habit formation in incomplete semimartingale markets," Papers 1112.2940, arXiv.org, revised May 2015.
    2. 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.
    3. Peter Bank & Helena Kauppila, 2014. "Convex duality for stochastic singular control problems," Papers 1407.7717, arXiv.org.
    4. Markus Mocha & Nicholas Westray, 2011. "The Stability of the Constrained Utility Maximization Problem - A BSDE Approach," Papers 1107.0190, arXiv.org.
    5. Oleksii Mostovyi, 2015. "Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption," Finance and Stochastics, Springer, vol. 19(1), pages 135-159, January.
    6. Kardaras, Constantinos, 2010. "Numéraire-invariant preferences in financial modeling," LSE Research Online Documents on Economics 44993, London School of Economics and Political Science, LSE Library.
    7. repec:spr:compst:v:63:y:2006:i:1:p:123-150 is not listed on IDEAS
    8. Constantinos Kardaras, 2009. "Num\'{e}raire-invariant preferences in financial modeling," Papers 0903.3736, arXiv.org, revised Nov 2010.
    9. repec:bla:mathfi:v:27:y:2017:i:1:p:68-95 is not listed on IDEAS
    10. Salvatore Federico & Paul Gassiat & Fausto Gozzi, 2015. "Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation," Finance and Stochastics, Springer, vol. 19(2), pages 415-448, April.
    11. Constantinos Kardaras & Jan Obłój & Eckhard Platen, 2017. "The Numéraire Property And Long-Term Growth Optimality For Drawdown-Constrained Investments," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 68-95, January.
    12. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    13. Ying Jiao & Huyên Pham, 2011. "Optimal investment with counterparty risk: a default-density model approach," Finance and Stochastics, Springer, vol. 15(4), pages 725-753, December.
    14. Giulia Di Nunno & Steffen Sjursen, 2013. "Information and optimal investment in defaultable assets," Papers 1312.6032, arXiv.org.
    15. 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.
    16. Traian A Pirvu & Ulrich G Haussmann, 2007. "On Robust Utility Maximization," Papers math/0702727, arXiv.org.
    17. Holger Kraft & Mogens Steffensen, 2006. "Portfolio problems stopping at first hitting time with application to default risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 123-150, February.

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