2008/02/10 by Ashkan Nikeghbali, Nikeghbali, Ashkan
Economics, Econometrics and Finance · Mathematics · #05C38 #15A15 (Primary) #15A18 (Secondary) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:05C38 #msc:15A15 #msc:15A18
paper · pdf · doi:10.48550/arxiv.0802.1317
arxiv created 2008/02/10 · openalex publication_date 2008/02/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, using martingale techniques, we prove a generalization of Doob's maximal identity in the setting of continuous nonnegative local submartingales (Xt) of the form: Xt=Nt+At, where the measure (dAt) is carried by the set \t: Xt=0\. In particular, we give a multiplicative decomposition for the Azéma supermartingale associated with some last passage times related to such processes and we prove that these non-stopping times contain very useful information. As a consequence, we obtain the law of the maximum of a continuous nonnegative local martingale (Mt) which satisfies M_∞=ψ(supt≥0Mt) for some measurable function ψ as well as the law of the last time this maximum is reached.