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

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 pro...

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Bibliographic Details
Published in:arXiv.org 2023-01
Main Author: Savku, Emel
Format: Article
Language:English
Subjects:
Constraints
Differential games
Game theory
Lagrange multiplier
Maximum principle
Optimal control
Stochastic processes
Online Access:Get full text
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Summary: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.
ISSN:2331-8422