Representations and regularities for solutions to BSDEs with reflections

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:115

Article

Ma, J ; Zhang, JF

关键词: backward SDEs with reflections;    Feynman-Kac formulae;    path regularities;    pseudo-approximations;    L-2 -modulus;    Bermuda options;    rate of convergence;   

DOI  :  10.1016/j.spa.2004.05.010

来源: Elsevier

【 摘 要 】

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 C-1-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 L-2-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. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free