Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle
Abstract 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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer
2018-06-01
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| Series: | Probability, Uncertainty and Quantitative Risk |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s41546-018-0030-2 |
| Summary: | Abstract 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. |
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| ISSN: | 2367-0126 |