We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations (BSVIEs) with jumps, where path-dependence means the dependence of the free term and generator of a path of a càdlàg process. Furthermore, we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation (FSVIE) with jumps and a linear path-dependent BSVIE with jumps. As a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.

中文翻译：

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具有跳跃，微分和对偶原理的与路径相关的后向随机Volterra积分方程

我们研究带跳的路径相关的后向随机Volterra积分方程（BSVIE）解的存在性和唯一性，其中路径相关性意味着自由项和càdlàg过程路径生成器的依赖性。此外，我们证明了这种解决方案的路径可微性，并建立了带有跳跃的线性依赖于路径的正向随机Volterra积分方程（FSVIE）和带有跳跃的线性依赖于路径的BSVIE的对偶原理。由于对偶原理，我们得到了一个比较定理，并基于带有跳跃的路径相关BSVIE推导了一类动态相关风险度量。