Backward Stochastic Differential Equations with Double Mean Reflections

2023/07/12 by Hanwu Li, Li, Hanwu · 4 citations
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2307.05947

Abstract

In this paper, we study the backward stochastic differential equation (BSDE) with two nonlinear mean reflections, which means that the constraints are imposed on the distribution of the solution but not on its paths. Based on the backward Skorokhod problem with nonlinear constraints, we obtain the existence and uniqueness result by constructing a contraction mapping. When the constraints are linear, the solution can be approximated by a family of penalized mean-field BSDEs.

Cited by

• Conditional Expectation Backward Stochastic Differential Equations and Related Backward Stochastic Differential Equations with Conditional Reflection
• Backward Stochastic Differential Equations with Nonlinear Expectation Reflection
• Mean-field BSDEs with non-Lipschitz coefficients and double mean reflections
• Quadratic BSDEs with double constraints driven by G-Brownian motion

Related

• Mean Field Backward Stochastic Differential Equations with Double Mean Reflections
• Mean Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Constraints
• Mean-field BSDEs with non-Lipschitz coefficients and double mean reflections
• Backward Stochastic Differential Equations with Nonlinear Expectation Reflection
• Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Reflections