SOLVABILITY AND NUMERICAL SIMULATION OF BSDEs RELATED TO BSPDEs WITH APPLICATIONS TO UTILITY MAXIMIZATION
AbstractIn this paper we study BSDEs arising from a special class of backward stochastic partial differential equations (BSPDEs) that is intimately related to utility maximization problems with respect to arbitrary utility functions. After providing existence and uniqueness we discuss the numerical realizability. Then we study utility maximization problems on incomplete financial markets whose dynamics are governed by continuous semimartingales. Adapting standard methods that solve the utility maximization problem using BSDEs, we give solutions for the portfolio optimization problem which involve the delivery of a liability at maturity. We illustrate our study by numerical simulations for selected examples. As a byproduct we prove existence of a solution to a very particular quadratic growth BSDE with unbounded terminal condition. This complements results on this topic obtained in Briand and Hu (2006, 2008) and Briand et al. (2007).
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Bibliographic InfoArticle provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.
Volume (Year): 14 (2011)
Issue (Month): 05 ()
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Web page: http://www.worldscinet.com/ijtaf/ijtaf.shtml
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- Ulrich Horst & Ying Hu & Peter Imkeller & Anthony Reveillac, 2011. "Forward-backward systems for expected utility maximization," SFB 649 Discussion Papers SFB649DP2011-061, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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