Representations and regularities for solutions to BSDEs with reflections

Jin Ma and Jianfeng Zhang

Stochastic Processes and their Applications, 2005, vol. 115, issue 4, 539-569

Abstract: In this paper we study a class of backward stochastic differential equations with reflections (BSDER, for short). Three types of discretization procedures are introduced in the spirit of the so-called Bermuda Options in finance, so as to first establish a Feynman-Kac type formula for the martingale integrand of the BSDER, and then to derive the continuity of the paths of the martingale integrand, as well as the C1-regularity of the solution to a corresponding obstacle problem. We also introduce a new notion of regularity for a stochastic process, which we call the "L2-modulus regularity". Such a regularity is different from the usual path regularity in the literature, and we show that such regularity of the martingale integrand produces exactly the rate of convergence of a numerical scheme for BSDERs. Both numerical scheme and its rate of convergence are novel.

Keywords: Backward; SDEs; with; reflections; Feynman-Kac; formulae; Path; regularities; Pseudo-approximations; L2-modulus; Bermuda; options; Rate; of; convergence (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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