Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles

2015/02/10 by Roxana Dumitrescu, Dumitrescu, Roxana, Céline Labart +1
Economics, Econometrics and Finance · Computer Science · Biochemistry, Genetics and Molecular Biology · #Stochastic processes and financial applications #Advanced Mathematical Modeling in Engineering #Diffusion and Search Dynamics

paper · doi:10.48550/arxiv.1502.02888

Abstract

We introduce a discrete time reflected scheme to solve doubly reflected Backward Stochastic Differential Equations with jumps (in short DRBSDEs), driven by a Brownian motion and an independent compensated Poisson process. As in Dumitrescu-Labart (2014), we approximate the Brownian motion and the Poisson process by two random walks, but contrary to this paper, we discretize directly the DRBSDE, without using a penalization step. This gives us a fully implementable scheme, which only depends on one parameter of approximation: the number of time steps n (contrary to the scheme proposed in Dumitrescu-Labart (2014), which also depends on the penalization parameter). We prove the convergence of the scheme, and give some numerical examples.

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