Stochastic control for Backward Stochastic Differential Equations with semi-Markov chain noises

2025/12/20 by Robert J. Elliott, Zhe Yang, Elliott, Robert J. +1
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.2512.18218

openalex publication_date 2025/12/20 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we extend the results of Elliott and Yang \citeelliott3 and discuss the control of a stochastic process for which the driving noise is provided by a martingale associated with a semi-Markov Chain. An existence and a comparison theorem are obtained. In our discrete time setting, adjoint processes are provided by backward stochastic difference equations. Technical results from partial differential equation theory to establish a verification theorem are not required.

Citations

• Comparison and converse comparison theorems for backward stochastic differential equations with Markov chain noise

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