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Optimal consumption and investment with bounded downside risk measures for logarithmic utility functions

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  • Claudia Kluppelberg

    (LMRS)

  • Serguei Pergamenchtchikov

    (LMRS)

Abstract

We investigate optimal consumption problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall for logarithmic utility functions. We find the solutions in terms of a dynamic strategy in explicit form, which can be compared and interpreted. This paper continues our previous work, where we solved similar problems for power utility functions.

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  • Claudia Kluppelberg & Serguei Pergamenchtchikov, 2010. "Optimal consumption and investment with bounded downside risk measures for logarithmic utility functions," Papers 1002.2486, arXiv.org.
    • Handle: RePEc:arx:papers:1002.2486
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    References listed on IDEAS

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    1. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    3. Susanne Emmer & Claudia Klüppelberg & Ralf Korn, 2001. "Optimal Portfolios with Bounded Capital at Risk," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 365-384, October.
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