IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2001.10108.html
   My bibliography  Save this paper

Stochastic control of optimized certainty equivalents

Author

Listed:
  • Julio Backhoff Veraguas
  • A. Max Reppen
  • Ludovic Tangpi

Abstract

Optimized certainty equivalents (OCEs) is a family of risk measures widely used by both practitioners and academics. This is mostly due to its tractability and the fact that it encompasses important examples, including entropic risk measures and average value at risk. In this work we consider stochastic optimal control problems where the objective criterion is given by an OCE risk measure, or put in other words, a risk minimization problem for controlled diffusions. A major difficulty arises since OCEs are often time inconsistent. Nevertheless, via an enlargement of state space we achieve a substitute of sorts for time consistency in fair generality. This allows us to derive a dynamic programming principle and thus recover central results of (risk-neutral) stochastic control theory. In particular, we show that the value of our risk minimization problem can be characterized via the viscosity solution of a Hamilton--Jacobi--Bellman--Issacs equation. We further establish the uniqueness of the latter under suitable technical conditions.

Suggested Citation

  • Julio Backhoff Veraguas & A. Max Reppen & Ludovic Tangpi, 2020. "Stochastic control of optimized certainty equivalents," Papers 2001.10108, arXiv.org, revised Jun 2022.
    • Handle: RePEc:arx:papers:2001.10108
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2001.10108
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    2. Georg Ch. Pflug & Alois Pichler, 2016. "Time-Consistent Decisions and Temporal Decomposition of Coherent Risk Functionals," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 682-699, May.
    3. Pflug, Georg Ch. & Pichler, Alois, 2016. "Time-inconsistent multistage stochastic programs: Martingale bounds," European Journal of Operational Research, Elsevier, vol. 249(1), pages 155-163.
    4. Nicole Bäuerle & Jonathan Ott, 2011. "Markov Decision Processes with Average-Value-at-Risk criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 361-379, December.
    5. Aharon Ben‐Tal & Marc Teboulle, 2007. "An Old‐New Concept Of Convex Risk Measures: The Optimized Certainty Equivalent," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 449-476, July.
    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. Gechun Liang & Yifan Sun & Thaleia Zariphopoulou, 2023. "Representation of forward performance criteria with random endowment via FBSDE and application to forward optimized certainty equivalent," Papers 2401.00103, arXiv.org.

    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. Yuanying Guan & Zhanyi Jiao & Ruodu Wang, 2022. "A reverse ES (CVaR) optimization formula," Papers 2203.02599, arXiv.org, revised May 2023.
    2. Simone Cerreia†Vioglio & Lars Peter Hansen & Fabio Maccheroni & Massimo Marinacci, 2020. "Making Decisions under Model Misspecification," Working Papers 2020-103, Becker Friedman Institute for Research In Economics.
    3. Daniel Bartl & Samuel Drapeau & Ludovic Tangpi, 2017. "Computational aspects of robust optimized certainty equivalents and option pricing," Papers 1706.10186, arXiv.org, revised Mar 2019.
    4. Aharon Ben-Tal & Dimitris Bertsimas & David B. Brown, 2010. "A Soft Robust Model for Optimization Under Ambiguity," Operations Research, INFORMS, vol. 58(4-part-2), pages 1220-1234, August.
    5. Dan A. Iancu & Marek Petrik & Dharmashankar Subramanian, 2015. "Tight Approximations of Dynamic Risk Measures," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 655-682, March.
    6. Nicole Bäuerle & Ulrich Rieder, 2014. "More Risk-Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 105-120, February.
    7. Samuel Drapeau & Michael Kupper, 2013. "Risk Preferences and Their Robust Representation," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 28-62, February.
    8. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
    9. Julio Backhoff & Ulrich Horst, 2014. "Conditional Analysis and a Principal-Agent problem," Papers 1412.4698, arXiv.org, revised Jun 2016.
    10. Černý, Aleš & Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2012. "On the computation of optimal monotone mean–variance portfolios via truncated quadratic utility," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 386-395.
    11. Nicole Bauerle & Alexander Glauner, 2020. "Distributionally Robust Markov Decision Processes and their Connection to Risk Measures," Papers 2007.13103, arXiv.org.
    12. Denis Belomestny & Tobias Hübner & Volker Krätschmer, 2022. "Solving optimal stopping problems under model uncertainty via empirical dual optimisation," Finance and Stochastics, Springer, vol. 26(3), pages 461-503, July.
    13. Christopher W. Miller & Insoon Yang, 2015. "Optimal Control of Conditional Value-at-Risk in Continuous Time," Papers 1512.05015, arXiv.org, revised Jan 2017.
    14. Seungki Min & Ciamac C. Moallemi & Costis Maglaras, 2022. "Risk-Sensitive Optimal Execution via a Conditional Value-at-Risk Objective," Papers 2201.11962, arXiv.org.
    15. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
    16. Laeven, R.J.A. & Stadje, M.A., 2011. "Entropy Coherent and Entropy Convex Measures of Risk," Discussion Paper 2011-031, Tilburg University, Center for Economic Research.
    17. Jarrod Burgh & Emerson Melo, 2023. "Wishful Thinking is Risky Thinking," Papers 2307.02422, arXiv.org, revised Feb 2024.
    18. Nicole Bäuerle & Alexander Glauner, 2021. "Minimizing spectral risk measures applied to Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 35-69, August.
    19. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
    20. Nicole Bauerle & Alexander Glauner, 2020. "Minimizing Spectral Risk Measures Applied to Markov Decision Processes," Papers 2012.04521, arXiv.org.

    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:2001.10108. 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.