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

Ludger Overbeck1, Jasmin A. L. Röder1
1Institute of Mathematics, University of Gießen, 35392 Gießen, Germany

Tóm tắt

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.

Tài liệu tham khảo

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