IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v312y2022i2d10.1007_s10479-020-03768-5.html
   My bibliography  Save this article

Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market

Author

Listed:
  • E. Savku

    (Middle East Technical University
    École Polytechnique, CMAP)

  • G.-W Weber

    (Middle East Technical University
    Poznan University of Technology)

Abstract

We apply dynamic programming principle to discuss two optimal investment problems by using zero-sum and nonzero-sum stochastic game approaches in a continuous-time Markov regime-switching environment within the frame work of behavioral finance. We represent different states of an economy and, consequently, investors’ floating levels of psychological reactions by a D-state Markov chain. The first application is a zero-sum game between an investor and the market, and the second one formulates a nonzero-sum stochastic differential portfolio game as the sensitivity of two investors’ terminal gains. We derive regime-switching Hamilton–Jacobi–Bellman–Isaacs equations and obtain explicit optimal portfolio strategies with Feynman–Kac representations of value functions. We illustrate our results in a two-state special case and observe the impact of regime switches by comparative results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:312:y:2022:i:2:d:10.1007_s10479-020-03768-5
    DOI: 10.1007/s10479-020-03768-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-020-03768-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-020-03768-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Korn, Ralf & Melnyk, Yaroslav & Seifried, Frank Thomas, 2017. "Stochastic impulse control with regime-switching dynamics," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1024-1042.
    2. Kourtidis, Dimitrios & Šević, Željko & Chatzoglou, Prodromos, 2011. "Investors’ trading activity: A behavioural perspective and empirical results," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 40(5), pages 548-557.
    3. Avanidhar Subrahmanyam, 2008. "Behavioural Finance: A Review and Synthesis," European Financial Management, European Financial Management Association, vol. 14(1), pages 12-29, January.
    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. El-Karoui, N. & Hamadène, S., 2003. "BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 145-169, September.
    6. George Loewenstein, 2000. "Emotions in Economic Theory and Economic Behavior," American Economic Review, American Economic Association, vol. 90(2), pages 426-432, May.
    7. Chang-Yi Li & Son-Nan Chen & Shih-Kuei Lin, 2016. "Pricing derivatives with modeling CO emission allowance using a regime-switching jump diffusion model: with regime-switching risk premium," The European Journal of Finance, Taylor & Francis Journals, vol. 22(10), pages 887-908, August.
    8. Dimitrios Kourtidis & Željko Ševi? & Prodromos Chatzoglou, 2011. "Investors' trading activity, a behavioural perspective: professionals vs. individuals," International Journal of Behavioural Accounting and Finance, Inderscience Enterprises Ltd, vol. 2(3/4), pages 346-366.
    9. Kuhnen, Camelia M. & Knutson, Brian, 2011. "The Influence of Affect on Beliefs, Preferences, and Financial Decisions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 46(3), pages 605-626, June.
    10. Olivier Menoukeu-Pamen & Romuald Hervé Momeya, 2017. "A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(3), pages 349-388, June.
    11. Samuel N. Cohen & Robert J. Elliott, 2008. "Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions," Papers 0810.0055, arXiv.org, revised Jan 2010.
    12. Olivier Menoukeu Pamen, 2017. "Maximum Principles of Markov Regime-Switching Forward–Backward Stochastic Differential Equations with Jumps and Partial Information," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 373-410, November.
    13. Hersh Shefrin & Meir Statman, 1993. "Behavioral Aspects of the Design and Marketing of Financial Products," Financial Management, Financial Management Association, vol. 22(2), Summer.
    14. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xu, Xiaoxiao & Yu, Hao & Sun, Qiuwen & Tam, Vivian W.Y., 2023. "A critical review of occupant energy consumption behavior in buildings: How we got here, where we are, and where we are headed," Renewable and Sustainable Energy Reviews, Elsevier, vol. 182(C).
    2. Koundouri, Phoebe & Papayiannis, Georgios I. & Petracou, Electra V. & Yannacopoulos, Athanasios N., 2023. "Consensus group decision making under model uncertainty with a view towards environmental policy making," MPRA Paper 122006, University Library of Munich, Germany.
    3. Shen, Jiayu & Shi, Yuanji & Shi, Jianxin & Dai, Yunzhong & Li, Wei, 2023. "An uncertain permutation flow shop predictive scheduling problem with processing interruption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    4. Taheri, Nima & Jahani, Hamed & Pishvaee, Mir Saman, 2024. "Modeling sustainable bioethanol supply chain in Australia: A system dynamics approach," Renewable Energy, Elsevier, vol. 227(C).
    5. P. Koundouri & G. I. Papayiannis & E. V. Petracou & A. N. Yannacopoulos, 2024. "Consensus Group Decision Making Under Model Uncertainty with a View Towards Environmental Policy Making," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 87(6), pages 1611-1649, June.

    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. Dimitrios Kourtidis & Željko Šević & Prodromos Chatzoglou, 2016. "Mood and stock returns: evidence from Greece," Journal of Economic Studies, Emerald Group Publishing Limited, vol. 43(2), pages 242-258, May.
    2. Yogita Singh & Mohd. Adil & S. M. Imamul Haque, 2023. "Personality traits and behaviour biases: the moderating role of risk-tolerance," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(4), pages 3549-3573, August.
    3. Zamri Ahmad & Haslindar Ibrahim & Jasman Tuyon, 2017. "Behavior of fund managers in Malaysian investment management industry," Qualitative Research in Financial Markets, Emerald Group Publishing Limited, vol. 9(3), pages 205-239, August.
    4. Samahita, Margaret & Holm, Håkan J., 2020. "Mining for Mood Effect in the Field," Working Papers 2020:2, Lund University, Department of Economics.
    5. Bachar FAKHRY, 2016. "A Regime Switching Explanation of the Reactions of Market Participant during the Crisis," Journal of Economics Bibliography, KSP Journals, vol. 3(3), pages 434-449, September.
    6. Aren Selim & Hamamci Hatice Nayman, 2023. "Mediating Effect of Pleasure-Seeking and Loss Aversion in the Relationship Between Phantasy and Financial Risk Tolerance and the Moderating Role of Confidence," Folia Oeconomica Stetinensia, Sciendo, vol. 23(2), pages 24-44, December.
    7. Kiss, Hubert J. & Rodriguez-Lara, Ismael & Rosa-Garcia, Alfonso, 2014. "Do women panic more than men? An experimental study of financial decisions," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 52(C), pages 40-51.
    8. Miklánek, Tomáš & Zajíček, Miroslav, 2020. "Personal traits and trading in an experimental asset market," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 86(C).
    9. Muhammad Arsalan Hashmi & M Abdullah & Tariq Jalees & Ume Amen & Muhammad Arsalan, 2023. "Do Personality Traits and Cultural Norms Influence Investment Decisions? The Role of Financial Literacy and Investor Overconfidence," Journal of Economic Impact, Science Impact Publishers, vol. 5(1), pages 106-113.
    10. Adler, Matthew D. & Dolan, Paul & Henwood, Amanda & Kavetsos, Georgios, 2022. "“Better the devil you know”: Are stated preferences over health and happiness determined by how healthy and happy people are?," Social Science & Medicine, Elsevier, vol. 303(C).
    11. Muhammad Nauman Sadiq, Raja Ased Azad Khan, 2019. "Impact of Personality Traits on Investment Intention: The Mediating Role of Risk Behaviour and the Moderating Role of Financial Literacy," Journal of Finance and Economics Research, Geist Science, Iqra University, Faculty of Business Administration, vol. 4(1), pages 1-18, March.
    12. Halko, Marja Liisa & Kaustia, Markku, 2012. "Are risk preferences dynamic? Within-subject variation in risk-taking as a function of background music," CFS Working Paper Series 2012/09, Center for Financial Studies (CFS).
    13. Rodwell Kufakunesu & Calisto Guambe, 2018. "On the optimal investment-consumption and life insurance selection problem with an external stochastic factor," Papers 1808.04608, arXiv.org.
    14. Anzel van den Bergh-Lindeque & Sune Ferreira-Schenk & Zandri Dickason-Koekemoer, 2021. "Individual Investor Risk Tolerance from a Behavioural Finance Perspective in Gauteng, South Africa," International Journal of Economics and Financial Issues, Econjournals, vol. 11(4), pages 53-65.
    15. Wettstein, Dominik J. & Boes, Stefan, 2022. "How value-based policy interventions influence price negotiations for new medicines: An experimental approach and initial evidence," Health Policy, Elsevier, vol. 126(2), pages 112-121.
    16. Saggese, Pietro & Belmonte, Alessandro & Dimitri, Nicola & Facchini, Angelo & Böhme, Rainer, 2023. "Arbitrageurs in the Bitcoin ecosystem: Evidence from user-level trading patterns in the Mt. Gox exchange platform," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 251-270.
    17. Apergis, Nicholas & Hayat, Tasawar & Kadasah, Nasser A., 2019. "Subjective well-being in housing purchasing: Evidence with survey data from the U.K. housing residential market," The Quarterly Review of Economics and Finance, Elsevier, vol. 74(C), pages 328-335.
    18. Zamri Ahmad & Haslindar Ibrahim & Jasman Tuyon, 2017. "Institutional investor behavioral biases: syntheses of theory and evidence," Management Research Review, Emerald Group Publishing Limited, vol. 40(5), pages 578-603, May.
    19. Osman Sayid Hassan Musse & Abdelghani Echchabi & Hassanuddeen Abdul Aziz, 2015. "Islamic and Conventional Behavioral Finance: A Critical Review of Literature التمويل السلوكي الإسلامي والتقليدي: مراجعة نقدية للأدبيات," Journal of King Abdulaziz University: Islamic Economics, King Abdulaziz University, Islamic Economics Institute., vol. 28(2), pages 237-251, July.
    20. Berrada, Tony & Detemple, Jérôme & Rindisbacher, Marcel, 2018. "Asset pricing with beliefs-dependent risk aversion and learning," Journal of Financial Economics, Elsevier, vol. 128(3), pages 504-534.

    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:spr:annopr:v:312:y:2022:i:2:d:10.1007_s10479-020-03768-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.