Path-Dependent Backward Stochastic Volterra Integral Equations with Jumps, Differentiability and Duality Principle

39 Pages Posted: 12 Sep 2016 Last revised: 21 Apr 2018

See all articles by Ludger Overbeck

Ludger Overbeck

University of Giessen

Jasmin Röder

University of Giessen

Date Written: April 12, 2018

Abstract

We study existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations (BSVIEs, in short) 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, in short) 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.

Keywords: path-dependent backward stochastic Volterra integral equation; jump diffusion; path-differentiability; duality principle

Suggested Citation

Overbeck, Ludger and Röder, Jasmin, Path-Dependent Backward Stochastic Volterra Integral Equations with Jumps, Differentiability and Duality Principle (April 12, 2018). Available at SSRN: https://ssrn.com/abstract=2836961 or http://dx.doi.org/10.2139/ssrn.2836961

Ludger Overbeck

University of Giessen ( email )

Institut of Mathematics
Giessen, 35394
Germany

Jasmin Röder (Contact Author)

University of Giessen ( email )

Arndtstr. 2
Giessen, 35392
Germany

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