2015/12/12 by Anna Aksamit, Aksamit, Anna, Monique Jeanblanc +3
Economics, Econometrics and Finance · Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1512.03992
openalex publication_date 2015/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We work in the setting of the progressive enlargement mathbb G of a\nreference filtration mathbb F through the observation of a random time\n\τ. We study an integral representation property for some classes of\n mathbb G-martingales stopped at \τ. In the first part, we focus on the\ncase where mathbb F is a Poisson filtration and we establish a predictable\nrepresentation property with respect to three mathbb G-martingales. In the\nsecond part, we relax the assumption that mathbb F is a Poisson filtration\nand we assume that \τ is an mathbb F-pseudo-stopping time. We establish\nintegral representations with respect to some mathbb G-martingales built\nfrom mathbb F-martingales and, under additional hypotheses, we obtain a\npredictable representation property with respect to two mathbb\nG-martingales.\n