2011/01/01 by Anthony Réveillac, Anthony Reveillac, Reveillac, Anthony
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.1108.3965
arxiv created 2011/08/19 · openalex publication_date 2011/08/19 · arxiv updated 2011/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove that every random variable of the form F(MT) with F:\reald →\real a Borelian map and M a d-dimensional continuous Markov martingale with respect to a Markov filtration F admits an exact integral representation with respect to M, that is, without any orthogonal component. This representation holds true regardless any regularity assumption on F. We extend this result to Markovian quadratic growth BSDEs driven by M and show they can be solved without an orthogonal component. To this end, we extend first existence results for such BSDEs under a general filtration and then obtain regularity properties such as differentiability for the solution process.