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Convergence of utility functions and convergence of optimal strategies

Author

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  • Clotilde Napp

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Elyès Jouini

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper we study the stability (in the L p as well as for the almost sure convergence sense) of the optimal investment-consumption strategy with respect to the choice of the utility function.

Suggested Citation

  • Clotilde Napp & Elyès Jouini, 2004. "Convergence of utility functions and convergence of optimal strategies," Post-Print halshs-00151579, HAL.
    • Handle: RePEc:hal:journl:halshs-00151579
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00151579
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    Cited by:

    1. Pietro Siorpaes, 2015. "Optimal investment and price dependence in a semi-static market," Finance and Stochastics, Springer, vol. 19(1), pages 161-187, January.
    2. Pazdera, Jaroslav & Schumacher, Johannes M. & Werker, Bas J.M., 2016. "Cooperative investment in incomplete markets under financial fairness," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 394-406.
    3. Michail Anthropelos & Gordan Žitković, 2010. "Partial equilibria with convex capital requirements: existence, uniqueness and stability," Annals of Finance, Springer, vol. 6(1), pages 107-135, January.
    4. Laurence Carassus & Miklós Rásonyi, 2007. "Optimal Strategies and Utility-Based Prices Converge When Agents’ Preferences Do," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 102-117, February.
    5. Lingqi Gu & Yiqing Lin & Junjian Yang, 2017. "Utility maximization problem under transaction costs: optimal dual processes and stability," Papers 1710.04363, arXiv.org.
    6. Gordan Žitković, 2012. "An example of a stochastic equilibrium with incomplete markets," Finance and Stochastics, Springer, vol. 16(2), pages 177-206, April.
    7. Markus Mocha & Nicholas Westray, 2011. "The Stability of the Constrained Utility Maximization Problem - A BSDE Approach," Papers 1107.0190, arXiv.org.
    8. Larsen, Kasper & Zitkovic, Gordan, 2007. "Stability of utility-maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1642-1662, November.
    9. Nicole Bäuerle & Ulrich Rieder, 2009. "MDP algorithms for portfolio optimization problems in pure jump markets," Finance and Stochastics, Springer, vol. 13(4), pages 591-611, September.
    10. Niu, Liqun, 2008. "Some stability results of optimal investment in a simple Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 445-452, February.
    11. Gordan Zitkovic, 2009. "An example of a stochastic equilibrium with incomplete markets," Papers 0906.0208, arXiv.org, revised Jun 2010.
    12. Kasper Larsen, 2009. "Continuity Of Utility‐Maximization With Respect To Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 237-250, April.
    13. Xing, Hao, 2017. "Stability of the exponential utility maximization problem with respect to preferences," LSE Research Online Documents on Economics 57213, London School of Economics and Political Science, LSE Library.
    14. Hao Xing, 2012. "Stability of the exponential utility maximization problem with respect to preferences," Papers 1205.6160, arXiv.org, revised Sep 2013.
    15. Michail Anthropelos & Gordan Zitkovic, 2009. "Partial Equilibria with Convex Capital Requirements: Existence, Uniqueness and Stability," Papers 0901.3318, arXiv.org.
    16. Gino Favero & Tiziano Vargiolu, 2006. "Shortfall risk minimising strategies in the binomial model: characterisation and convergence," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 237-253, October.
    17. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
    18. Hyungbin Park, 2021. "Influence of risk tolerance on long-term investments: A Malliavin calculus approach," Papers 2104.00911, arXiv.org.
    19. Constantinos Kardaras & Gordan Zitkovic, 2007. "Stability of the utility maximization problem with random endowment in incomplete markets," Papers 0706.0482, arXiv.org, revised Mar 2010.

    More about this item

    Keywords

    optimal investment strategies; robustnes properties;

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