Stochastic differential equations with respect to optional semimartingales and two reflecting regulated barriers

2022/02/25 by Astrid Hilbert, Hilbert, Astrid, Imane Jarni +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.2202.12862

arxiv created 2022/02/25 · openalex publication_date 2022/02/25 · arxiv updated 2022/02/28 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this work, we introduce a new Skorokhod problem with two reflecting barriers when the trajectories of the driven process and the barriers are right and left limited. We show that this problem has an explicit unique solution in a deterministic case. Then, we apply our result to study the existence and uniqueness of solutions of reflected stochastic differential equations with respect to optional semimartingales. The study is carried out on a probability space that does not necessarily satisfy the usual conditions.

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