Reflected backward stochastic differential equations with time-delayed generators

Abstract

This paper is devoted to establish an existence and uniqueness result of one-dimensional reflected backward stochastic differential equations with time-delayed generators (RBSDEs with time-delayed generators, in short). Our proof is based on approximation via a penalization method.

Backward Stochastic Volterra Integral Equations With Non-Lipschitz Time Delayed Generators

“…Since then, the study of BSDEs with delayed generators has been intensified. The work of Dos Reis et al (Dos Reis & al., 2012), Zhou and Ren (Zhou & Ren, 2012), Tuo et al (Tuo & al., 2018) and references therein attest this statement. More recently, Coulibaly and Aman (Coulibaly & Aman, 2019) have studied new class of BSDEs having the form…”

“…Concerning delayed BSDE, see [4] for non-Lipschitz condition and [8,9] in the context of finance and assurance. For reflected delayed BSDE see [34] and [26].…”

$L^{p}$-solutions of backward stochastic differential equations with time-delayed generators

“…Coulibaly and Aman, [2], Tuo et al, [9] and Dos Reis et al, [6]. All this works have been done under p-integrability condition ( p ≥ 2) on the data { f (t, 0, 0)} t∈[0,T] and ξ.…”

Backward stochastic differential equations with time-delayed generators and integrable parameters

“…Since this three results, a lot of works concerned the delayed BSDEs have been done in literature. Among others one can cite these works of Ren et al, [13], Coulibaly and Aman, [2], Tuo et al, [12], Dos Reis et al, [6] and Ren et al [11]. In all this works, existence and uniqueness result are provided under delayed Lipschitz or non-Lipschitz condition with p-integrable data, for p > 1.…”