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A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem

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  • Morlais, Marie-Amelie

Abstract

In this study, we consider the exponential utility maximization problem in the context of a jump-diffusion model. To solve this problem, we rely on the dynamic programming principle to express the value process of this problem in terms of the solution of a quadratic BSDE with jumps. Since the quadratic BSDE1 under study is driven by both a Wiener process and a Poisson random measure having a Lévy measure with infinite mass, our main task is therefore to establish a new existence result for the specific BSDE introduced.

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  • Morlais, Marie-Amelie, 2010. "A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1966-1995, September.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:10:p:1966-1995
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    References listed on IDEAS

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    1. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    2. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276, April.
    3. Royer, Manuela, 2006. "Backward stochastic differential equations with jumps and related non-linear expectations," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1358-1376, October.
    4. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Papers math/0508489, arXiv.org.
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