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A Stochastic Control Approach for Constrained Stochastic Differential Games with Jumps and Regimes

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  • Emel Savku

    (Department of Mathematics, University of Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway)

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 types 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 the 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.

Suggested Citation

  • Emel Savku, 2023. "A Stochastic Control Approach for Constrained Stochastic Differential Games with Jumps and Regimes," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3043-:d:1190001
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    References listed on IDEAS

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    1. Chaoqun Ma & Hui Wu & Xiang Lin, 2015. "Nonzero-Sum Stochastic Differential Portfolio Games under a Markovian Regime Switching Model," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-18, February.
    2. Robert Elliott & Tak Siu, 2010. "On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy," Annals of Operations Research, Springer, vol. 176(1), pages 271-291, April.
    3. Peng, Jin-Lung & Jeng, Vivian & Wang, Jennifer L. & Chen, Yen-Chih, 2017. "The impact of bancassurance on efficiency and profitability of banks: Evidence from the banking industry in Taiwan," Journal of Banking & Finance, Elsevier, vol. 80(C), pages 1-13.
    4. Emel Savku & Gerhard-Wilhelm Weber, 2018. "A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 696-721, November.
    5. Milijana Novovic Buric & Vladimir Kascelan & Sasa Vujosevic, 2015. "Bancassurance Concept From The Perspective Of Montenegrin Market," Economic Review: Journal of Economics and Business, University of Tuzla, Faculty of Economics, vol. 13(2), pages 62-73, November.
    6. Shen, Yang & Siu, Tak Kuen, 2013. "Stochastic differential game, Esscher transform and general equilibrium under a Markovian regime-switching Lévy model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 757-768.
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    Cited by:

    1. Nikolai Chemetov & Fernanda Cipriano, 2024. "A Boundary Control Problem for Stochastic 2D-Navier–Stokes Equations," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1847-1879, November.

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