2022/10/11 by Peter Imkeller, Imkeller, Peter, Rhoss Likibi Pellat +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.2210.05622
In this paper, we consider quadratic forward-backward SDEs (QFBSDEs), for which the drift in the forward equation does not satisfy the standard globally Lipschitz condition and the driver of the backward system possesses nonlinearity of type f(|y|)|z|2, where f is any locally integrable function. We prove both the Malliavin and classical derivative of the QFBSDE and provide representations of these processes. We study a numerical approximation of this system in the sense of \citeImkDosReis in which the authors assume that the drift is Lipschitz and the driver of the BSDE is quadratic in the traditional sense (i.e., f is a positive constant). We show that the rate of convergence is the same as in \citeImkDosReis