IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1503.01802.html
   My bibliography  Save this paper

Game-theoretic approach to risk-sensitive benchmarked asset management

Author

Listed:
  • Amogh Deshpande
  • Saul D. Jacka

Abstract

In this article we consider a game theoretic approach to the Risk-Sensitive Benchmarked Asset Management problem (RSBAM) of Davis and Lleo \cite{DL}. In particular, we consider a stochastic differential game between two players, namely, the investor who has a power utility while the second player represents the market which tries to minimize the expected payoff of the investor. The market does this by modulating a stochastic benchmark that the investor needs to outperform. We obtain an explicit expression for the optimal pair of strategies as for both the players.

Suggested Citation

  • Amogh Deshpande & Saul D. Jacka, 2015. "Game-theoretic approach to risk-sensitive benchmarked asset management," Papers 1503.01802, arXiv.org.
    • Handle: RePEc:arx:papers:1503.01802
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1503.01802
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    2. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bäuerle, Nicole & Rieder, Ulrich, 2017. "Zero-sum risk-sensitive stochastic games," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 622-642.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. S'ebastien Lleo & Wolfgang J. Runggaldier, 2023. "On the Separation of Estimation and Control in Risk-Sensitive Investment Problems under Incomplete Observation," Papers 2304.08910, arXiv.org, revised Nov 2023.
    2. Mark H.A. Davis & Sébastien Lleo, 2021. "Risk‐sensitive benchmarked asset management with expert forecasts," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1162-1189, October.
    3. Aleksandr G. Alekseev & Mikhail V. Sokolov, 2016. "Benchmark-based evaluation of portfolio performance: a characterization," Annals of Finance, Springer, vol. 12(3), pages 409-440, December.
    4. Aleksandr Alekseev & Mikhail Sokolov, 2016. "Portfolio Return Relative to a Benchmark," EUSP Department of Economics Working Paper Series 2016/04, European University at St. Petersburg, Department of Economics.
    5. Alexander Alekseev & Mikhail Sokolov, 2016. "Portfolio Return Relative to a Benchmark," EUSP Department of Economics Working Paper Series Ec-04/16, European University at St. Petersburg, Department of Economics.
    6. Chendi Ni & Yuying Li & Peter A. Forsyth, 2023. "Neural Network Approach to Portfolio Optimization with Leverage Constraints:a Case Study on High Inflation Investment," Papers 2304.05297, arXiv.org, revised May 2023.
    7. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen & Erik Schlögl, 2009. "Alternative Defaultable Term Structure Models," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(1), pages 1-31, March.
    8. Shankar, Ravi & Goel, Mayank, 2024. "Risk-sensitive benchmarked portfolio optimization under non-linear market dynamics," Applied Mathematics and Computation, Elsevier, vol. 481(C).
    9. Sebastien Lleo & Wolfgang Runggaldier, 2025. "Exploratory Randomization for Discrete-Time Linear Exponential Quadratic Gaussian (LEQG) Problem," Papers 2501.06275, arXiv.org.
    10. Carole Bernard & Franck Moraux & Ludger R�schendorf & Steven Vanduffel, 2015. "Optimal payoffs under state-dependent preferences," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1157-1173, July.
    11. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 19-38.
    12. Vladimir Cherny & Jan Obłój, 2013. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Finance and Stochastics, Springer, vol. 17(4), pages 771-800, October.
    13. repec:uts:finphd:40 is not listed on IDEAS
    14. Constantinos Kardaras, 2009. "Num\'{e}raire-invariant preferences in financial modeling," Papers 0903.3736, arXiv.org, revised Nov 2010.
    15. Eckhard Platen & Renata Rendek, 2009. "Simulation of Diversified Portfolios in a Continuous Financial Market," Research Paper Series 264, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Mikhail Zhitlukhin, 2018. "Survival investment strategies in a continuous-time market model with competition," Papers 1811.12491, arXiv.org, revised Sep 2019.
    17. Eberlein, Ernst & Kabanov, Yuri & Schmidt, Thorsten, 2022. "Ruin probabilities for a Sparre Andersen model with investments," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 72-84.
    18. Christina Nikitopoulos-Sklibosios & Eckhard Platen, 2012. "Alternative Term Structure Models for Reviewing Expectations Puzzles," Research Paper Series 305, Quantitative Finance Research Centre, University of Technology, Sydney.
    19. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
    20. Mikhail Zhitlukhin, 2022. "A continuous-time asset market game with short-lived assets," Finance and Stochastics, Springer, vol. 26(3), pages 587-630, July.
    21. Claudio Fontana, 2015. "Weak And Strong No-Arbitrage Conditions For Continuous Financial Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-34.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1503.01802. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.