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Article Dans Une Revue Statistics and Probability Letters Année : 2011

On the orthogonal component of BSDEs in a Markovian setting

Résumé

In this note we consider a quadratic growth backward stochastic differential equation (BSDE) driven by a continuous martingale M. We prove (in Theorem 3.2) that if M is a strong Markov process and if the BSDE has the form (2.2) 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.

Dates et versions

hal-00635484 , version 1 (25-10-2011)

Identifiants

Citer

Anthony Réveillac. On the orthogonal component of BSDEs in a Markovian setting. Statistics and Probability Letters, 2011, 82 (1), pp.Pages 151-157. ⟨10.1016/j.spl.2011.09.015⟩. ⟨hal-00635484⟩
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