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

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  • Hiroaki Hata
  • Hideo Nagai
  • Shuenn-Jyi Sheu
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    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.

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    File URL: http://arxiv.org/pdf/1001.2131
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1001.2131.

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    Date of creation: Jan 2010
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    Publication status: Published in Annals of Applied Probability 2010, Vol. 20, No. 1, 52-89
    Handle: RePEc:arx:papers:1001.2131

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    Web page: http://arxiv.org/

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    1. Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, Elsevier, vol. 116(1-2), pages 365-386.
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    Cited by:
    1. Hiroaki Hata, 2011. "“Down-Side Risk” Probability Minimization Problem with Cox-Ingersoll-Ross’s Interest Rates," Asia-Pacific Financial Markets, Springer, Springer, vol. 18(1), pages 69-87, March.
    2. Huyen Pham, 2014. "Long time asymptotics for optimal investment," Papers 1408.6455, arXiv.org.
    3. Huyen Pham, 2014. "Long time asymptotics for optimal investment," Working Papers, HAL hal-01058657, HAL.
    4. Ichihara, Naoyuki, 2012. "Large time asymptotic problems for optimal stochastic control with superlinear cost," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 122(4), pages 1248-1275.
    5. Tadashi Hayashi & Jun Sekine, 2011. "Risk-sensitive Portfolio Optimization with Two-factor Having a Memory Effect," Asia-Pacific Financial Markets, Springer, Springer, vol. 18(4), pages 385-403, November.
    6. Watanabe, Yûsuke, 2013. "Asymptotic analysis for a downside risk minimization problem under partial information," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 123(3), pages 1046-1082.

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