Path-dependent backward stochastic Volterra integral equations with jumps,differentiability and duality principle  

作　　者：Ludger Overbeck Jasmin A.L.Roder 

机构地区：[1]Institute of Mathematics,University of Gießen,Arndtsraße 2,35392 Gießen,Germany

出　　处：《Probability, Uncertainty and Quantitative Risk》2018年第1期109-145,共37页概率、不确定性与定量风险（英文）

摘　　要：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 c`adl`ag 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.

关 键 词：Path-dependent backward stochastic Volterra integral equation Jump diffusion Path-differentiability Duality principle Comparison theorem Functional Ito formula Dynamic coherent risk measure 

分 类 号：O17[理学—数学]