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Optimal consumption and investment with bounded downside risk for power utility functions

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  • Claudia Kluppelberg

    (LMRS)

  • Serguei Pergamenchtchikov

    (LMRS)

Abstract

We investigate optimal consumption and investment problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall. We formulate various utility maximization problems, which can be solved explicitly. We compare the optimal solutions in form of optimal value, optimal control and optimal wealth to analogous problems under additional uniform risk bounds. Our proofs are partly based on solutions to Hamilton-Jacobi-Bellman equations, and we prove a corresponding verification theorem. This work was supported by the European Science Foundation through the AMaMeF programme.

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  • Claudia Kluppelberg & Serguei Pergamenchtchikov, 2010. "Optimal consumption and investment with bounded downside risk for power utility functions," Papers 1002.2487, arXiv.org.
    • Handle: RePEc:arx:papers:1002.2487
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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. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    3. 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.
    4. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    5. 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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