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March 2010 Backward SDEs with constrained jumps and quasi-variational inequalities
Idris Kharroubi, Jin Ma, Huyên Pham, Jianfeng Zhang
Ann. Probab. 38(2): 794-840 (March 2010). DOI: 10.1214/09-AOP496


We consider a class of backward stochastic differential equations (BSDEs) driven by Brownian motion and Poisson random measure, and subject to constraints on the jump component. We prove the existence and uniqueness of the minimal solution for the BSDEs by using a penalization approach. Moreover, we show that under mild conditions the minimal solutions to these constrained BSDEs can be characterized as the unique viscosity solution of quasi-variational inequalities (QVIs), which leads to a probabilistic representation for solutions to QVIs. Such a representation in particular gives a new stochastic formula for value functions of a class of impulse control problems. As a direct consequence, this suggests a numerical scheme for the solution of such QVIs via the simulation of the penalized BSDEs.


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Idris Kharroubi. Jin Ma. Huyên Pham. Jianfeng Zhang. "Backward SDEs with constrained jumps and quasi-variational inequalities." Ann. Probab. 38 (2) 794 - 840, March 2010.


Published: March 2010
First available in Project Euclid: 9 March 2010

zbMATH: 1205.60114
MathSciNet: MR2642892
Digital Object Identifier: 10.1214/09-AOP496

Primary: 35K85 , 60H10 , 60H30

Keywords: backward stochastic differential equation , impulse control problems , jump constraints , jump-diffusion process , Penalization , quasi-variational inequalities , viscosity solutions

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 2 • March 2010
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