Backward stochastic differential equations with non‐Lipschitz time delayed generators

Abstract

In this paper, we establish the existence and uniqueness result for a class of backward stochastic differential equations (BSDEs, in short) with non-Lipschitz time delayed generators. In our point of view, this work is a non trivial extension of the pioneer result obtained by Delong and Imkeller under global Lipschitz condition. Indeed, for certain generators our result is valid while their result can not be hold.

$L^{p}$-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.…”

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

“…Next, for type-II BSVIEs see [27] and [16] for results in the L p sense. 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].…”