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<p>We study backward stochastic differential equations (BSDEs) with jumps with mean-field type heterogeneous interactions governed by graphons, and associated dynamic risk measures. We prove existence, uniqueness and measurability results of solutions of these systems under some regularity assumptions and provide moment estimates. Under additional conditions, comparison theorems are obtained. Continuity and stability of such systems are also established. We then prove convergence of finite interacting mean-field particle systems with heterogeneous interactions to graphon mean-field BSDEs. Finally, we introduce the graphon dynamic risk measure induced by the solution of a graphon mean-field BSDE system and study its properties. In particular, a dual representation theorem is provided in the convex case.</p>

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Graphon mean-field backward stochastic differential equations with jumps and associated dynamic risk measures

  • 期刊论文

  • 发表日期：

    2025年9月15日

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  • Hamed Amini,
  • Zhongyuan Cao,
  • Agnès Sulem

摘要

We study backward stochastic differential equations (BSDEs) with jumps with mean-field type heterogeneous interactions governed by graphons, and associated dynamic risk measures. We prove existence, uniqueness and measurability results of solutions of these systems under some regularity assumptions and provide moment estimates. Under additional conditions, comparison theorems are obtained. Continuity and stability of such systems are also established. We then prove convergence of finite interacting mean-field particle systems with heterogeneous interactions to graphon mean-field BSDEs. Finally, we introduce the graphon dynamic risk measure induced by the solution of a graphon mean-field BSDE system and study its properties. In particular, a dual representation theorem is provided in the convex case.