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

2025/11/10 by Tao Hao, Ying Hu, Hao, Tao +3
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Nonlinear Differential Equations Analysis #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2511.07173

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 \mathscrQ(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 \mathscrO(N^-(1)/(2λ)), where λ>1.

Citations

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• On the rate of convergence in Wasserstein distance of the empirical\n measure
• Mean-Field Backward Stochastic Volterra Integral Equations
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Related

• Mean-field stochastic Volterra equations
• Mean-Field Backward Stochastic Volterra Integral Equations
• Singular mean-field backward stochastic Volterra integral equations in infinite dimensional spaces
• Mean-field backward stochastic differential equations and nonlocal PDEs with quadratic growth
• Existence, uniqueness and propagation of chaos for general McKean-Vlasov and mean-field BSDEs