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Optimal portfolio policies under bounded expected loss and partial information

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  • Jörn Sass
  • Ralf Wunderlich

Abstract

In a market with partial information we consider the optimal selection of portfolios for utility maximizing investors under joint budget and shortfall risk constraints. The shortfall risk is measured in terms of expected loss. Stock returns satisfy a stochastic differential equation. Under general conditions on the corresponding drift process we provide the optimal trading strategy using Malliavin calculus. We give extensive numerical results in the case that the drift is modeled as a continuous-time Markov chain with finitely many states. To deal with the problem of time-discretization when applying the results to market data, we propose a method to detect and correct possible tracking errors. Copyright Springer-Verlag 2010

Suggested Citation

  • Jörn Sass & Ralf Wunderlich, 2010. "Optimal portfolio policies under bounded expected loss and partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 25-61, August.
    • Handle: RePEc:spr:mathme:v:72:y:2010:i:1:p:25-61
    DOI: 10.1007/s00186-010-0300-y
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    References listed on IDEAS

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    8. L.C.G. Rogers, 2001. "The relaxed investor and parameter uncertainty," Finance and Stochastics, Springer, vol. 5(2), pages 131-154.
    9. 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.
    10. A. Gabih & W. Grecksch & M. Richter & R. Wunderlich, 2006. "Optimal portfolio strategies benchmarking the stock market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 211-225, October.
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    Citations

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    Cited by:

    1. Rudiger Frey & Abdelali Gabih & Ralf Wunderlich, 2013. "Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach," Papers 1303.2513, arXiv.org, revised Feb 2014.
    2. Kristoffer Lindensjö, 2016. "Optimal investment and consumption under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 87-107, February.
    3. Bäuerle Nicole & Gilitschenski Igor & Hanebeck Uwe, 2015. "Exact and approximate hidden Markov chain filters based on discrete observations," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 159-176, December.
    4. Kristoffer Lindensjö, 2016. "Optimal investment and consumption under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 87-107, February.
    5. Chen, An & Hieber, Peter & Nguyen, Thai, 2019. "Constrained non-concave utility maximization: An application to life insurance contracts with guarantees," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1119-1135.
    6. Nicole Bauerle & An Chen, 2022. "Optimal investment under partial information and robust VaR-type constraint," Papers 2212.04394, arXiv.org, revised Sep 2023.
    7. An Chen & Thai Nguyen & Mitja Stadje, 2018. "Risk management with multiple VaR constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 297-337, October.
    8. Nicole Bauerle & Igor Gilitschenski & Uwe D. Hanebeck, 2014. "Exact and Approximate Hidden Markov Chain Filters Based on Discrete Observations," Papers 1411.0849, arXiv.org, revised Dec 2014.

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