Mean-field backward stochastic Volterra integral equations: well-posedness and related particle system

TL;DR

This paper investigates the well-posedness of mean-field backward stochastic Volterra integral equations (BSVIEs) with linear and quadratic growth conditions and analyzes the convergence rates of associated particle systems.

Contribution

It establishes existence, uniqueness, and propagation of chaos for mean-field BSVIEs with new growth conditions and derives explicit convergence rates for particle systems.

Findings

Existence and uniqueness of solutions for mean-field BSVIEs with linear and quadratic growth.

Propagation of chaos for particle systems under specified conditions.

Convergence rates of order (N) and (N^{-rac{1}{2\u03bb}}) for particle systems.

Abstract

This paper studies the mean-field backward stochastic Volterra integral equations (mean-field BSVIEs) and associated particle systems. We establish the existence and uniqueness of solutions to mean-field BSVIEs when the generator $g$ is of linear growth or quadratic growth with respect to $Z$, respectively. Moreover, the propagation of chaos is analyzed for the corresponding particle systems under two conditions. When $g$ is of linear growth in $Z$, the convergence rate is proven to be of order $\mathscr{Q}(N)$. When $g$ is of quadratic growth in $Z$ and is independent of the law of $Z$, we not only establish the convergence of the particle systems but also derive a convergence rate of order $\mathscr{O}(N^{-\frac{1}{2\lambda}})$, where $\lambda>1$.