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On the orthogonal component of BSDEs in a Markovian setting

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  • Réveillac, Anthony

Abstract

In this note we consider a quadratic growth backward stochastic differential equation (BSDE) driven by a continuous martingale M. We prove (in ) that if M is a strong Markov process and if the BSDE has the form with regular data 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) (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.

Suggested Citation

  • Réveillac, Anthony, 2012. "On the orthogonal component of BSDEs in a Markovian setting," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 151-157.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:1:p:151-157
    DOI: 10.1016/j.spl.2011.09.015
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    References listed on IDEAS

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    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    2. Marie-Amélie Morlais, 2009. "Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem," Finance and Stochastics, Springer, vol. 13(1), pages 121-150, January.
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