Optimal consumption and investment with bounded downside risk for power utility functions
AbstractWe 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1002.2487.
Date of creation: Feb 2010
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-02-27 (All new papers)
- NEP-RMG-2010-02-27 (Risk Management)
- NEP-UPT-2010-02-27 (Utility Models & Prospect Theory)
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- Suleyman Basak & Alex Shapiro, . "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," Rodney L. White Center for Financial Research Working Papers 6-99, Wharton School Rodney L. White Center for Financial Research.
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