IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i14p3043-d1190001.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/14/3043/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/14/3043/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. E. Savku & G.-W Weber, 2022. "Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market," Annals of Operations Research, Springer, vol. 312(2), pages 1171-1196, May.
    2. Vaneet Bhatia & Sankarshan Basu & Subrata Kumar Mitra & Pradyumna Dash, 2018. "A review of bank efficiency and productivity," OPSEARCH, Springer;Operational Research Society of India, vol. 55(3), pages 557-600, November.
    3. Chen, Jianxin & Zheng, Junhao & Zhang, Tonghua & Hou, Rui & Zhou, Yong-wu, 2022. "Dynamical complexity of pricing and green level for a dyadic supply chain with capital constraint," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 1-21.
    4. Phung, Manh-Trung & Cheng, Cheng-Ping & Guo, Chuanyin & Kao, Chen-Yu, 2020. "Mixed Network DEA with Shared Resources: A Case of Measuring Performance for Banking Industry," Operations Research Perspectives, Elsevier, vol. 7(C).
    5. Godin, Frédéric & Lai, Van Son & Trottier, Denis-Alexandre, 2019. "Option pricing under regime-switching models: Novel approaches removing path-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 130-142.
    6. Qi, Yue & Liao, Kezhi & Liu, Tongyang & Zhang, Yu, 2022. "Originating multiple-objective portfolio selection by counter-COVID measures and analytically instigating robust optimization by mean-parameterized nondominated paths," Operations Research Perspectives, Elsevier, vol. 9(C).
    7. Gu Wang & Jiaxuan Ye, 2023. "Fund Managers’ Competition for Investment Flows Based on Relative Performance," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 605-643, August.
    8. Benjamín Vallejo Jiménez & Francisco Venegas Martínez, 2017. "Optimal consumption and portfolio rules when the asset price is driven by a time-inhomogeneous Markov modulated fractional Brownian motion with," Economics Bulletin, AccessEcon, vol. 37(1), pages 314-326.
    9. Kai Zheng & Weidong Xu & Xili Zhang, 2023. "Multivariate Regime Switching Model Estimation and Asset Allocation," Computational Economics, Springer;Society for Computational Economics, vol. 61(1), pages 165-196, January.
    10. Liao, Chang-Sheng, 2023. "Deregulation, bank efficiency and economic cooperation across China–Taiwan Strait," Journal of Policy Modeling, Elsevier, vol. 45(2), pages 430-444.
    11. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Pricing annuity guarantees under a double regime-switching model," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 62-78.
    12. Lirong Cui & Quan Zhang & Dejing Kong, 2016. "Some New Concepts and Their Computational Formulae in Aggregated Stochastic Processes with Classifications Based on Sojourn Times," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 999-1019, December.
    13. Kozak Sylwester & Wierzbowska Agata, 2021. "Banking Market Concentration and Bank Efficiency. Evidence from Southern, Eastern and Central Europe," South East European Journal of Economics and Business, Sciendo, vol. 16(1), pages 38-52, June.
    14. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2017. "Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 46-62.
    15. Ivana Marinovic Matovic, 2019. "Bancassurance: Challenges and Opportunities in Republic of Serbia," Proceedings of the 13th International RAIS Conference, June 10-11, 2019 08IM, Research Association for Interdisciplinary Studies.
    16. Jakub Trybuła & Dariusz Zawisza, 2019. "Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences—Stochastic Factor Case," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 966-987, August.
    17. Cheng, Maoyong & Qu, Yang, 2023. "The false prosperity and promising future: Effects of data resources on bank efficiency," International Review of Financial Analysis, Elsevier, vol. 89(C).
    18. Jerzy Grobelny & Rafal Michalski & Gerhard-Wilhelm Weber, 2021. "Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic," WORking papers in Management Science (WORMS) WORMS/21/09, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.
    19. Lucia Reis Peixoto Roselli & Leydiana de Sousa Pereira & Anderson Lucas Carneiro de Lima Silva & Adiel Teixeira Almeida & Danielle Costa Morais & Ana Paula Cabral Seixas Costa, 2020. "Neuroscience experiment applied to investigate decision-maker behavior in the tradeoff elicitation procedure," Annals of Operations Research, Springer, vol. 289(1), pages 67-84, June.
    20. Siyu Lv & Zhen Wu & Qing Zhang, 2022. "The Dynkin game with regime switching and applications to pricing game options," Annals of Operations Research, Springer, vol. 313(2), pages 1159-1182, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3043-:d:1190001. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.