IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2105.07915.html
   My bibliography  Save this paper

Hedging Goals

Author

Listed:
  • Thomas Krabichler
  • Marcus Wunsch

Abstract

Goal-based investing is concerned with reaching a monetary investment goal by a given finite deadline, which differs from mean-variance optimization in modern portfolio theory. In this article, we expand the close connection between goal-based investing and option hedging that was originally discovered in [Bro99b] by allowing for varying degrees of investor risk aversion using lower partial moments of different orders. Moreover, we show that maximizing the probability of reaching the goal (quantile hedging, cf. [FL99]) and minimizing the expected shortfall (efficient hedging, cf. [FL00]) yield, in fact, the same optimal investment policy. We furthermore present an innovative and model-free approach to goal-based investing using methods of reinforcement learning. To the best of our knowledge, we offer the first algorithmic approach to goal-based investing that can find optimal solutions in the presence of transaction costs.

Suggested Citation

  • Thomas Krabichler & Marcus Wunsch, 2021. "Hedging Goals," Papers 2105.07915, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2105.07915
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2105.07915
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482.
    2. Johannes Ruf & Weiguan Wang, 2019. "Neural networks for option pricing and hedging: a literature review," Papers 1911.05620, arXiv.org, revised May 2020.
    3. Eckhard Platen, 2005. "On The Role Of The Growth Optimal Portfolio In Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 365-388, December.
    4. Oleg Szehr, 2021. "Hedging of Financial Derivative Contracts via Monte Carlo Tree Search," Papers 2102.06274, arXiv.org, revised Apr 2021.
    5. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    Full references (including those not matched with items on IDEAS)

    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. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    2. Ilhan, Aytaç & Jonsson, Mattias & Sircar, Ronnie, 2009. "Optimal static-dynamic hedges for exotic options under convex risk measures," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3608-3632, October.
    3. Balder, Sven & Brandl, Michael & Mahayni, Antje, 2009. "Effectiveness of CPPI strategies under discrete-time trading," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 204-220, January.
    4. Zhou, Qing & Wu, Weixing & Wang, Zengwu, 2008. "Cooperative hedging with a higher interest rate for borrowing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 609-616, April.
    5. Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.
    6. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    7. François, Pascal & Gauthier, Geneviève & Godin, Frédéric, 2014. "Optimal hedging when the underlying asset follows a regime-switching Markov process," European Journal of Operational Research, Elsevier, vol. 237(1), pages 312-322.
    8. Dominick Samperi, 2002. "Calibrating a Diffusion Pricing Model with Uncertain Volatility: Regularization and Stability," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 71-87, January.
    9. Peter Lindberg, 2012. "Optimal partial hedging of an American option: shifting the focus to the expiration date," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(3), pages 221-243, June.
    10. Lukas Gonon & Christoph Schwab, 2021. "Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models," Finance and Stochastics, Springer, vol. 25(4), pages 615-657, October.
    11. Blanka Horvath & Josef Teichmann & Žan Žurič, 2021. "Deep Hedging under Rough Volatility," Risks, MDPI, vol. 9(7), pages 1-20, July.
    12. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    13. Patrice Gaillardetz & Saeb Hachem, 2019. "Risk-Control Strategies," Papers 1908.02228, arXiv.org.
    14. Patrick Büchel & Michael Kratochwil & Maximilian Nagl & Daniel Rösch, 2022. "Deep calibration of financial models: turning theory into practice," Review of Derivatives Research, Springer, vol. 25(2), pages 109-136, July.
    15. Liao Wang & David D. Yao, 2021. "Risk Hedging for Production Planning," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1825-1837, June.
    16. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2022. "Deep Stochastic Optimization in Finance," Papers 2205.04604, arXiv.org.
    17. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep equal risk pricing of financial derivatives with non-translation invariant risk measures," Papers 2107.11340, arXiv.org.
    18. Michael J. Klass & Krzysztof Nowicki, 2010. "On The Consumption/Distribution Theorem Under The Long-Run Growth Criterion Subject To A Drawdown Constraint," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 931-957.
    19. Leitner Johannes, 2007. "Pricing and hedging with globally and instantaneously vanishing risk," Statistics & Risk Modeling, De Gruyter, vol. 25(4/2007), pages 1-22, October.
    20. Daniel Hernández-Hernández & Erick Treviño-Aguilar, 2014. "Characterization of the Value Process in Robust Efficient Hedging," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 56-75, April.

    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:2105.07915. 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.