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Asymptotics of the probability of minimizing 'down-side' risk under partial information

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  • Hideo Nagai

Abstract

We consider minimizing the probability of falling below a target growth rate of the wealth process up to a time horizon T in an incomplete market model under partial information and then study the asymptotic behavior of the minimizing probability as T → ∞. This problem is closely related to an ergodic risk-sensitive stochastic control problem under partial information in the risk-averse case. Indeed, in our main theorem we relate the former problem to the latter as its dual. As a result we obtain an explicit expression for the limit value of the former problem in the case of linear Gaussian models.

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  • 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.
    • Handle: RePEc:taf:quantf:v:11:y:2011:i:5:p:789-803
    DOI: 10.1080/14697680903341814
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    References listed on IDEAS

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    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..
    2. Hiroaki Hata & Yasunari Iida, 2006. "A risk-sensitive stochastic control approach to an optimal investment problem with partial information," Finance and Stochastics, Springer, vol. 10(3), pages 395-426, September.
    3. Hiroaki Hata & Hideo Nagai & Shuenn-Jyi Sheu, 2010. "Asymptotics of the probability minimizing a "down-side" risk," Papers 1001.2131, arXiv.org.
    4. W. H. Fleming & S. J. Sheu, 2000. "Risk‐Sensitive Control and an Optimal Investment Model," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 197-213, April.
    5. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
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    Cited by:

    1. 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.
    2. Hiroaki Hata, 2021. "Risk-Sensitive Asset Management with Lognormal Interest Rates," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(2), pages 169-206, June.
    3. Jun Sekine, 2012. "Long-term optimal portfolios with floor," Finance and Stochastics, Springer, vol. 16(3), pages 369-401, July.

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