On the orthogonal component of BSDEs in a Markovian setting

2009/07/06 by Anthony Réveillac, Réveillac, Anthony · 1 citation
Economics, Econometrics and Finance · Mathematics · #Nonlinear Differential Equations Analysis #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.0907.1071

6 pages

arxiv created 2009/07/06 · arxiv updated 2009/12/01

Abstract

In this Note we consider a quadratic backward stochastic differential equation (BSDE) driven by a continuous martingale M and whose generator is a deterministic function. We prove (in Theorem \reftheorem:main) that if M is a strong homogeneous Markov process and if the BSDE has the form \eqrefBSDE then the unique solution (Y,Z,N) of the BSDE is reduced to (Y,Z), i.e. the orthogonal martingale N is equal to zero showing that in a Markovian setting the "usual" solution (Y,Z) has not to be completed by a strongly orthogonal even if M does not enjoy the martingale representation property.

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• Weak martingale representation for continuous Markov processes and application to quadratic growth BSDEs

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