A stochastic control approach for constrained stochastic differential games with jumps and regimes

2023/01/30 by Emel Savku, Savku, Emel · 1 citation
Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2301.12921

openalex publication_date 2023/01/30 · openalex created_date 2023/02/01 · openalex updated_date 2026/07/28

Abstract

We develop an approach for two player constraint zero-sum and nonzero-sum stochastic differential games, which are modeled by Markov regime-switching jump-diffusion processes. We provide the relations between a usual stochastic optimal control setting and a Lagrangian method. In this context, we prove corresponding theorems for two different type of constraints, which lead us to find real valued and stochastic Lagrange multipliers, respectively. Then, we illustrate our results for a nonzero-sum game problem with stochastic maximum principle technique. Our application is an example of cooperation between a bank and an insurance company, which is a popular, well-known business agreement type, called Bancassurance.

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