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Simulation of BSDEs with jumps by Wiener Chaos Expansion

2016

International audience; We present an algorithm to solve BSDEs with jumps based on Wiener Chaos Expansion and Picard's iterations. This paper extends the results given in Briand-Labart (2014) to the case of BSDEs with jumps. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. Concerning the error, we derive explicit bounds with respect to the number of chaos, the discretization time step and the number of Monte Carlo simulations. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.

Statistics and ProbabilityWiener Chaos expansionDiscretizationMonte Carlo methodTime stepConditional expectation01 natural sciences010104 statistics & probabilitybackward stochastic differential equations with jumpsFOS: MathematicsApplied mathematics60H10 60J75 60H35 65C05 65G99 60H070101 mathematicsMathematicsPolynomial chaosApplied MathematicsNumerical analysis010102 general mathematicsMathematical analysista111Probability (math.PR)numerical methodCHAOS (operating system)[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]Modeling and SimulationScheme (mathematics)Mathematics - Probability
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