SOLVABILITY AND NUMERICAL SIMULATION OF BSDEs RELATED TO BSPDEs WITH APPLICATIONS TO UTILITY MAXIMIZATION

Peter Imkeller (), Anthony Réveillac () and Jianing Zhang ()
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Peter Imkeller: Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
Anthony Réveillac: Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
Jianing Zhang: Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2011, vol. 14, issue 05, 635-667

Abstract: In 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).

Keywords: BSDE; BSPDE; logarithmic transformation; distortion; quadratic growth; utility optimization; stochastic optimal control; numerical scheme (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0219024911006437

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