On the orthogonal component of BSDEs in a Markovian setting
Please always quote using this URN:urn:nbn:de:0296-matheon-7216
- In this Note we consider a Lipschitz backward stochastic differential equation (BSDE) driven by a continuous martingale $M$. We prove (in Theorem \ref{theorem:main}) that if $M$ is a strong Markov process and if the BSDE has regular data then the unique solution $(Y,Z,N)$ of the BSDE is reduced to $(Y,Z)$, \textit{i.e.} the orthogonal martingale $N$ is equal to zero, showing that in a Markovian setting the "usual" solution $(Y,Z)$ (of a BSDE with regular data) has not to be completed by a strongly orthogonal component even if $M$ does not enjoy the martingale representation property.
Author: | Anthony Réveillac |
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URN: | urn:nbn:de:0296-matheon-7216 |
Referee: | Dirk Becherer |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2010/06/10 |
Release Date: | 2010/06/10 |
Institute: | Humboldt-Universität zu Berlin |
Preprint Number: | 730 |