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

  • Claudia Kluppelberg

    (LMRS)

  • Serguei Pergamenchtchikov

    (LMRS)

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    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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    File URL: http://arxiv.org/pdf/1002.2487
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    Paper provided by arXiv.org in its series Papers with number 1002.2487.

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    Date of creation: Feb 2010
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    Handle: RePEc:arx:papers:1002.2487
    Contact details of provider: Web page: http://arxiv.org/

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    1. Susanne Emmer & Claudia Kl├╝ppelberg & Ralf Korn, 2001. "Optimal Portfolios with Bounded Capital at Risk," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 365-384.
    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.
    3. Suleyman Basak & Alexander Shapiro, 1999. "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-032, New York University, Leonard N. Stern School of Business-.
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