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Asymptotics for FBSDES with Jumps and Connections with Partial Integral Differential Equations

  • André de Oliveira Gomes
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 162)

Abstract

It is our intention to survey the asymptotic study of a certain class of coupled forward-backward stochastic differential equations (FBSDEs for short) when the noise terms in the forward diffusion have small intensities that converge to zero. The system of FBSDEs discussed can be used to give a probabilistic representation for the solution in the viscosity sense of an associated system of partial-integral differential equations (PIDEs) with a terminal condition. The asymptotic study of this PIDE is done probabilistically using the FBSDE system. Secondly we present a large deviations principle for the laws of the forward and backward processes of the stochastic system.

Keywords

FBSDEs with jumps Viscosity solutions Partial-integral differential equations Large deviations principles 

Notes

Acknowledgments

The author would like to thank the editors and the anonymous reviewers for their comments, suggestions and several corrections. The author acknowledges the financial support by the project IRTG 1740/ TRP 2011/50151-0 funded by the DFG/FAPESP.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Instititut für MathematikHumboldt-Universität zu BerlinBerlinGermany

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