A representation theorem for set-valued submartingales

2023/12/07 by Lục Trí Tuyên, Tuyen, Luc Tri, Vũ Thái Luân +1
Decision Sciences · #FOS: Mathematics #Probability (math.PR) #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2312.04006

openalex publication_date 2023/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The integral representation theorem for martingales has been widely used in probability theory. In this work, we propose and prove a general representation theorem for a class of set-valued submartingales. We also extend the stochastic integral representation for non-trivial initial set-valued martingales. Moreover, we show that this result covers the existing ones in the literature for both degenerated and non-degenerated set-valued martingales.

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