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

arXiv: https://arxiv.org/abs/2301.12921 · HTML: https://mlsanity.com/paper/2301.12921/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2023.

## Built on by (most cited first, 1 of 1)

- [Comparison of Deterministic and Probabilistic Machine Learning Algorithms for Precise Dimensional Control and Uncertainty Quantification in Additive Manufacturing](https://mlsanity.com/paper/2509.16233/) (2025)

## Abstract (arXiv)

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.