A unified approach to well-posedness of type-I backward stochastic Volterra integral equations

Mean-Field Backward Stochastic Volterra Integral Equations

Mean-field backward stochastic Volterra integral equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted Msolutions is established. Two duality principles between linear mean-field (forward) stochastic Volterra integral equations (MF-FSVIEs, for short) and MF-BSVIEs are obtained. Several comparison theorems for MF-FSVIEs and MF...

On Well - Posedness of Forward – Backward Sdes — a Unified Approach

In this paper, we study the well-posedness of the Forward–Backward Stochastic Differential Equations (FBSDE) in a general non-Markovian framework. The main purpose is to find a unified scheme which combines all existing methodology in the literature, and to address some fundamental longstanding problems for non-Markovian FBSDEs. An important device is a decoupling random field that is regular (...

Stochastic Volterra integral equations with a parameter

A wavelet method for stochastic Volterra integral equations and its application to general stock model

In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

Existence and Uniqueness of M-solutions for Backward Stochastic Volterra Integral Equations

In this article, we study general backward stochastic Volterra integral equations (BSVIEs). Combining the contractive-mapping principle, stepby-step iteration method and mathematical induction, we establish the existence and uniqueness theorem of M-solution for the BSVIEs. This theorem could be applied directly to many models, for example, using the result to a kind of financial models provides...