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Discrete time portfolio optimisation managing value at risk under heavy tail return distribution

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  • Subhojit Biswas
  • Diganta Mukherjee

Abstract

We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to the Value at Risk assuming a heavy tail distribution of the stock prices return. We use Markov Decision Process and dynamic programming principle to get the optimal strategies and the value function which maximize the expected utility for parametric as well as non parametric distributions. Due to lack of explicit solution in the non parametric case, we use numerical integration for optimization

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  • Subhojit Biswas & Diganta Mukherjee, 2019. "Discrete time portfolio optimisation managing value at risk under heavy tail return distribution," Papers 1908.03907, arXiv.org, revised Nov 2020.
    • Handle: RePEc:arx:papers:1908.03907
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    References listed on IDEAS

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    1. Fotios C. Harmantzis & Linyan Miao & Yifan Chien, 2006. "Empirical study of value-at-risk and expected shortfall models with heavy tails," Journal of Risk Finance, Emerald Group Publishing, vol. 7(2), pages 117-135, March.
    2. Lwin, Khin T. & Qu, Rong & MacCarthy, Bart L., 2017. "Mean-VaR portfolio optimization: A nonparametric approach," European Journal of Operational Research, Elsevier, vol. 260(2), pages 751-766.
    3. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    4. Young Kim & Rosella Giacometti & Svetlozar Rachev & Frank Fabozzi & Domenico Mignacca, 2012. "Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model," Annals of Operations Research, Springer, vol. 201(1), pages 325-343, December.
    5. repec:bla:jfinan:v:53:y:1998:i:2:p:499-547 is not listed on IDEAS
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