IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1001.2131.html
   My bibliography  Save this paper

Asymptotics of the probability minimizing a "down-side" risk

Author

Listed:
  • Hiroaki Hata
  • Hideo Nagai
  • Shuenn-Jyi Sheu

Abstract

We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation control problem. This problem will be shown to relate to a risk-sensitive stochastic control problem for a sufficiently large time horizon. Indeed, in our theorem we state a duality in the relation between the above two problems. Furthermore, under a multidimensional linear Gaussian model we obtain explicit solutions for the primal problem.

Suggested Citation

  • Hiroaki Hata & Hideo Nagai & Shuenn-Jyi Sheu, 2010. "Asymptotics of the probability minimizing a "down-side" risk," Papers 1001.2131, arXiv.org.
    • Handle: RePEc:arx:papers:1001.2131
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1001.2131
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michael Stutzer, 2011. "Portfolio choice with endogenous utility: a large deviations approach," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 43, pages 619-640, World Scientific Publishing Co. Pte. Ltd..
    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. Rongju Zhang & Nicolas Langrené & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2019. "Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method," Post-Print hal-02909342, HAL.
    2. Tadashi Hayashi & Jun Sekine, 2011. "Risk-sensitive Portfolio Optimization with Two-factor Having a Memory Effect," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(4), pages 385-403, November.
    3. Rongju Zhang & Nicolas Langren'e & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2017. "Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method," Papers 1704.00416, arXiv.org, revised Jun 2019.
    4. Hideo Nagai, 2011. "Asymptotics of the probability of minimizing 'down-side' risk under partial information," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 789-803.
    5. Watanabe, Yûsuke, 2013. "Asymptotic analysis for a downside risk minimization problem under partial information," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1046-1082.
    6. Anatolii A. Puhalskii & Michael Jay Stutzer, 2016. "On minimising a portfolio's shortfall probability," Papers 1602.02192, arXiv.org, revised May 2017.
    7. Ichihara, Naoyuki, 2012. "Large time asymptotic problems for optimal stochastic control with superlinear cost," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1248-1275.
    8. Hiroaki Hata, 2011. "“Down-Side Risk” Probability Minimization Problem with Cox-Ingersoll-Ross’s Interest Rates," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(1), pages 69-87, March.
    9. Huyen Pham, 2014. "Long time asymptotics for optimal investment," Papers 1408.6455, arXiv.org.
    10. Huyen Pham, 2014. "Long time asymptotics for optimal investment," Working Papers hal-01058657, HAL.

    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. Lars Peter Hansen & Jose A. Scheinkman, 2012. "Recursive utility in a Markov environment with stochastic growth," Working Papers 1380, Princeton University, Department of Economics, Econometric Research Program..
    2. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2020. "Portfolio selection with mental accounts: An equilibrium model with endogenous risk aversion," Journal of Banking & Finance, Elsevier, vol. 110(C).
    3. Christos I. Giannikos & Andreas Kakolyris, 2020. "Modelling the Blind Principal Bid Mechanism: A Large Deviation Approach," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 19(2), pages 187-200, September.
    4. Haley, M. Ryan & McGee, M. Kevin, 2006. "Tilting safety first and the Sharpe portfolio," Finance Research Letters, Elsevier, vol. 3(3), pages 173-180, September.
    5. Karen Benson & Philip Gray & Egon Kalotay & Judy Qiu, 2008. "Portfolio Construction and Performance Measurement when Returns are Non-Normal," Australian Journal of Management, Australian School of Business, vol. 32(3), pages 445-461, March.
    6. Haley, M. Ryan, 2008. "A simple nonparametric approach to low-dimension, shortfall-based portfolio selection," Finance Research Letters, Elsevier, vol. 5(3), pages 183-190, September.
    7. M. Ryan Haley, 2016. "Shortfall minimization and the Naive (1/N) portfolio: an out-of-sample comparison," Applied Economics Letters, Taylor & Francis Journals, vol. 23(13), pages 926-929, September.
    8. Alexis Bonnet & Isabelle Nagot, 2005. "Methodology of measuring performance in alternative investment," Cahiers de la Maison des Sciences Economiques b05078, Université Panthéon-Sorbonne (Paris 1).
    9. Georges Hübner & Thomas Lejeune, 2015. "Portfolio choice and investor preferences : A semi-parametric approach based on risk horizon," Working Paper Research 289, National Bank of Belgium.
    10. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, vol. 77(1), pages 177-234, January.
    11. Ji Cao & Marc Oliver Rieger & Lei Zhao, 2019. "Safety First, Loss Probability, and the Cross Section of Expected Stock Returns," Working Paper Series 2019-02, University of Trier, Research Group Quantitative Finance and Risk Analysis.
    12. Huyen Pham, 2007. "Some applications and methods of large deviations in finance and insurance," Papers math/0702473, arXiv.org, revised Feb 2007.
    13. Anatolii A. Puhalskii & Michael Jay Stutzer, 2016. "On minimising a portfolio's shortfall probability," Papers 1602.02192, arXiv.org, revised May 2017.
    14. M. Ryan Haley, 2018. "A nonparametric quantity-of-quality approach to assessing financial asset return performance," Annals of Finance, Springer, vol. 14(3), pages 343-351, August.
    15. Youngha Cho & Soosung Hwang & Steve Satchell, 2012. "The Optimal Mortgage Loan Portfolio in UK Regional Residential Real Estate," The Journal of Real Estate Finance and Economics, Springer, vol. 45(3), pages 645-677, October.
    16. Li, Zhongfei & Yao, Jing & Li, Duan, 2010. "Behavior patterns of investment strategies under Roy's safety-first principle," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(2), pages 167-179, May.
    17. Kim, Jang Ho & Kim, Woo Chang & Fabozzi, Frank J., 2013. "Composition of robust equity portfolios," Finance Research Letters, Elsevier, vol. 10(2), pages 72-81.
    18. Enrico Diecidue & Jeroen Van De Ven, 2008. "Aspiration Level, Probability Of Success And Failure, And Expected Utility," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(2), pages 683-700, May.
    19. repec:pri:metric:wp051_2013_hansen_scheinkman_stochastic-compounding-and-uncertain-valuati is not listed on IDEAS
    20. Djellout, Hacène & Guillin, Arnaud & Samoura, Yacouba, 2017. "Estimation of the realized (co-)volatility vector: Large deviations approach," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2926-2960.
    21. Alexis Bonnet & Isabelle Nagot, 2005. "Methodology of measuring performance in alternative investment," Post-Print halshs-00196443, HAL.

    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:1001.2131. 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.