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Asymptotic analysis for a downside risk minimization problem under partial information

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  • Watanabe, Yûsuke

Abstract

We give an analytic characterization of a large-time “downside risk” probability associated with an investor’s wealth. We assume that risky securities in our market model are affected by “hidden” economic factors, which evolve as a finite-state Markov chain. We formalize and prove a duality relation between downside risk minimization and the related risk-sensitive optimization. The proof is based on an analysis of an ergodic-type Hamilton–Jacobi–Bellman equation with large (exponentially growing) drift.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:3:p:1046-1082
    DOI: 10.1016/j.spa.2012.11.005
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    References listed on IDEAS

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    1. Stanley R. Pliska & Tomasz R. Bielecki, 2000. "Risk sensitive asset management with transaction costs," Finance and Stochastics, Springer, vol. 4(1), pages 1-33.
    2. 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.
    3. Hiroaki Hata & Hideo Nagai & Shuenn-Jyi Sheu, 2010. "Asymptotics of the probability minimizing a "down-side" risk," Papers 1001.2131, arXiv.org.
    4. Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
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    Cited by:

    1. 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.

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