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


  • Hiroaki Hata
  • Hideo Nagai
  • Shuenn-Jyi Sheu


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.

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

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    References listed on IDEAS

    1. Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 365-386.
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    Cited by:

    1. Rongju Zhang & Nicolas Langren'e & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2017. "Sharp Target Range Strategy for Multiperiod Portfolio Choice by Decensored Least Squares Monte Carlo," Papers 1704.00416,, revised Oct 2017.
    2. 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.
    3. 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.
    4. Huyen Pham, 2014. "Long time asymptotics for optimal investment," Papers 1408.6455,
    5. Anatolii A. Puhalskii & Michael Jay Stutzer, 2016. "On minimising a portfolio's shortfall probability," Papers 1602.02192,, revised May 2017.
    6. 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.
    7. 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.
    8. Huyen Pham, 2014. "Long time asymptotics for optimal investment," Working Papers hal-01058657, HAL.

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