1 February 2011
M. Bernhart, H. Pham, P. Tankov, X. Warin
We introduce a new of probabilistic method for solving a class of impulse control problems based on their representation as Backward Stochastic Differential Equations (BDSE) with constrained jumps. As an example, our method is used to price swing options. We deal with the jump contraints by a penalization procedure and apply a discrete-time backward scheme to the resulting penalized BSDE with jumps. We study the convergence of this numerical method with respect to the main approximation parameters: the jump intensity, the penalization parameter, and the time step. We present numerical tests and compare our results with a classical iteration methods.