In this paper, we provide a representation theorem for dynamic capital allocation under It{\^o}-L{\'e}vy model. We consider the representation of dynamic risk measures defined under Backward Stochastic Differential Equations (BSDE) with generators that grow quadratic-exponentially in the control variables. Dynamic capital allocation is derived from the differentiability of BSDEs with jumps. The results are illustrated by deriving a capital allocation representation for dynamic entropic risk measure and static coherent risk measure.

中文翻译：

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关于基于 BSDE 的动态风险度量和动态资本分配的表示的说明

在本文中，我们提供了 It{\^o}-L{\'e}vy 模型下动态资本配置的表示定理。我们考虑在后向随机微分方程 (BSDE) 下定义的动态风险度量的表示，其中生成器在控制变量中呈二次指数增长。动态资本分配源自具有跳跃的 BSDE 的可微性。通过导出动态熵风险度量和静态相干风险度量的资本分配表示来说明结果。