Solvability and numerical simulation of BSDEs related to BSPDEs with applications to utility maximization
Imkeller, Peter; Réveillac, Anthony; Zhang, Jianing (2011), Solvability and numerical simulation of BSDEs related to BSPDEs with applications to utility maximization, International Journal of Theoretical and Applied Finance, 14, 5, p. 635-667
TypeArticle accepté pour publication ou publié
Journal nameInternational Journal of Theoretical and Applied Finance
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Abstract (EN)In this paper we study BSDEs arising from a special class of backward stochastic partialdifferential equations (BSPDEs) that is intimately related to utility maximization problemswith respect to arbitrary utility functions. After providing existence and uniqueness we discuss the numerical realizability. Then we study utility maximization problems on incompletefinancial markets whose dynamics are governed by continuous semimartingales. Adaptingstandard methods that solve the utility maximization problem using BSDEs, we give solutions for the portfolio optimization problem which involve the delivery of a liability atmaturity. We illustrate our study by numerical simulations for selected examples. As abyproduct we prove existence of a solution to a very particular quadratic growth BSDE withunbounded terminal condition. This complements results on this topic obtained in [6, 7, 8].
Subjects / Keywordsstochastic optimal control; distortion transformation; utility optimization; quadratic growth; BSDE; logarithmic transformation; BSPDE; numerical scheme
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