On Cooperative Game Approaches For Optimal Portfolio Selection

Research Article
Open access

On Cooperative Game Approaches For Optimal Portfolio Selection

Zerong Chen 1*
  • 1 School of Mathematics, University of Edinburgh, Edinburgh, UK    
  • *corresponding author zerong_chen@outlook.com
Published on 24 April 2023 | https://doi.org/10.54254/2754-1169/5/20220075
AEMPS Vol.5
ISSN (Print): 2754-1177
ISSN (Online): 2754-1169
ISBN (Print): 978-1-915371-21-8
ISBN (Online): 978-1-915371-22-5

Abstract

Cooperative game theory is concerned with exploring schemes for allocating payoffs among rational participants in coalitions and has produced several solution designs due to the different emphasis on criteria such as stability and fairness, but this theory has not been widely applied in the field of portfolio selection. In this paper, we explore further applications of the solution concepts of cooperative games based on the model of optimal portfolio selection developed in previous studies, which is modelled in a static form of a non-cooperative zero-sum game between investors and the market and a cooperative game between investors. We propose a risk modified Shapley value based on the tradeoff between return and risk in the financial market based on the Shapley value, and the performance of this solution shows an evident improvement. We also introduce some other solution concepts of cooperative games and give an approach to construct a nucleolus-based portfolio using Maschler's scheme to compute the nucleolus, and the results demonstrate that the allocation schemes based on the cooperative game theory perform well.

Keywords:

Optimal Portfolio Selection, Cooperative Game Theory, Risk Modified Shapley Value, Nucleolus, Stock Market

Chen,Z. (2023). On Cooperative Game Approaches For Optimal Portfolio Selection. Advances in Economics, Management and Political Sciences,5,159-174.
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References

[1]. Markowits, H. M. (1952). Portfolio selection. Journal of finance, 7(1), 71-91.

[2]. Nash, J. F. (1951). Non-cooperative games.” Annals of Mathematics 54: 286-95.(1953). Two-person cooperative games." Econometrica, 21, 128-40.

[3]. Kocak, H. (2014). Canonical coalition game theory for optimal portfolio selection. Asian Economic and Financial Review, 4(9), 1254-1259.

[4]. Tataei, P., Roudposhti, F. R., Nikoumaram, H., and Hafezolkotob, A. (2018). Outperforming the market portfolio using coalitional game theory approach. Dama International Journal of Researchers, 3(5):145–155.

[5]. bin Ibrahim, M. A. R., Hee, P. C., Islam, M. A., & Bahaludin, H. (2020). Cooperative game theory approach for portfolio sectoral selection before and after Malaysia general elections: GE13 versus GE14.

[6]. Dai, J., & Xue, H. (2004). The strategy of profit allocation among partners in dynamic alliance based on the Shapley value. Chinese Journal of Management Science, 12(4), 33-36.

[7]. Fang, F., Yu, S., & Liu, M. (2020). An improved Shapley value-based profit allocation method for CHP-VPP. Energy, 213, 118805.

[8]. Xie, W., Yu, X., Zhang, Y., & Wang, H. (2020, July). An improved shapley value benefit distribution mechanism in cooperative game of cyber threat intelligence sharing. In IEEE INFOCOM 2020-IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS) (pp. 810-815). IEEE.

[9]. Singal, V. (2004). Beyond the random walk: A guide to stock market anomalies and low-risk investing. Oxford University Press, USA.

[10]. Schneider, P., Wagner, C., & Zechner, J. (2020). Low‐Risk Anomalies?. The Journal of finance, 75(5), 2673-2718.

[11]. Auer, B. R., & Hiller, T. (2019). Can cooperative game theory solve the low‐risk puzzle?. International Journal of Finance & Economics, 24(2), 884-889.

[12]. Shapley, L. S., & Shubik, M. (1973). Game Theory in Economics: Characteristic function, core, and stable set (Vol. 6). Rand.

[13]. Young, H. P., Okada, N., & Hashimoto, T. (1982). Cost allocation in water resources development. Water resources research, 18(3), 463-475.

[14]. Curiel, I. (2013). Cooperative game theory and applications: cooperative games arising from combinatorial optimization problems (Vol. 16). Springer Science & Business Media.

[15]. Maschler, M., Peleg, B., & Shapley, L. S. (1979). Geometric properties of the kernel, nucleolus, and related solution concepts. Mathematics of operations research, 4(4), 303-338.

[16]. Ben-Porath, E. (2014). Game Theory, Michael Maschler, Eilon Solan, Shmuel Zamir, Cambridge University Press (2013).

[17]. Durga, M. V. (2016). An efficient algorithm for solving nucleolus of cooperative TU games using MATLAB. Int. J. Innov. Res. Dev, 5.

[18]. Khudaykulova, M., Yuanqiong, H., & Khudaykulov, A. (2022). Economic consequences and implications of the Ukraine-russia war. International Journal of Management Science and Business Administration, 8(4), 44-52.

[19]. Mbah, R. E., & Wasum, D. F. (2022). Russian-Ukraine 2022 War: A review of the economic impact of Russian-Ukraine crisis on the USA, UK, Canada, and Europe. Advances in Social Sciences Research Journal, 9(3), 144-153.

Cite this article

Chen,Z. (2023). On Cooperative Game Approaches For Optimal Portfolio Selection. Advances in Economics, Management and Political Sciences,5,159-174.

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The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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About volume

Volume title: Proceedings of the 2022 International Conference on Financial Technology and Business Analysis (ICFTBA 2022), Part 1

ISBN：978-1-915371-21-8(Print) / 978-1-915371-22-5(Online)
Editor：Javier Cifuentes-Faura, Canh Thien Dang
Conference website: http://www.icftba.org
Conference date: 16 December 2022
Series: Advances in Economics, Management and Political Sciences
Volume number: Vol.5
ISSN：2754-1169(Print) / 2754-1177(Online)

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References

[1]. Markowits, H. M. (1952). Portfolio selection. Journal of finance, 7(1), 71-91.

[2]. Nash, J. F. (1951). Non-cooperative games.” Annals of Mathematics 54: 286-95.(1953). Two-person cooperative games." Econometrica, 21, 128-40.

[3]. Kocak, H. (2014). Canonical coalition game theory for optimal portfolio selection. Asian Economic and Financial Review, 4(9), 1254-1259.

[4]. Tataei, P., Roudposhti, F. R., Nikoumaram, H., and Hafezolkotob, A. (2018). Outperforming the market portfolio using coalitional game theory approach. Dama International Journal of Researchers, 3(5):145–155.

[5]. bin Ibrahim, M. A. R., Hee, P. C., Islam, M. A., & Bahaludin, H. (2020). Cooperative game theory approach for portfolio sectoral selection before and after Malaysia general elections: GE13 versus GE14.

[6]. Dai, J., & Xue, H. (2004). The strategy of profit allocation among partners in dynamic alliance based on the Shapley value. Chinese Journal of Management Science, 12(4), 33-36.

[7]. Fang, F., Yu, S., & Liu, M. (2020). An improved Shapley value-based profit allocation method for CHP-VPP. Energy, 213, 118805.

[8]. Xie, W., Yu, X., Zhang, Y., & Wang, H. (2020, July). An improved shapley value benefit distribution mechanism in cooperative game of cyber threat intelligence sharing. In IEEE INFOCOM 2020-IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS) (pp. 810-815). IEEE.

[9]. Singal, V. (2004). Beyond the random walk: A guide to stock market anomalies and low-risk investing. Oxford University Press, USA.

[10]. Schneider, P., Wagner, C., & Zechner, J. (2020). Low‐Risk Anomalies?. The Journal of finance, 75(5), 2673-2718.

[11]. Auer, B. R., & Hiller, T. (2019). Can cooperative game theory solve the low‐risk puzzle?. International Journal of Finance & Economics, 24(2), 884-889.

[12]. Shapley, L. S., & Shubik, M. (1973). Game Theory in Economics: Characteristic function, core, and stable set (Vol. 6). Rand.

[13]. Young, H. P., Okada, N., & Hashimoto, T. (1982). Cost allocation in water resources development. Water resources research, 18(3), 463-475.

[14]. Curiel, I. (2013). Cooperative game theory and applications: cooperative games arising from combinatorial optimization problems (Vol. 16). Springer Science & Business Media.

[15]. Maschler, M., Peleg, B., & Shapley, L. S. (1979). Geometric properties of the kernel, nucleolus, and related solution concepts. Mathematics of operations research, 4(4), 303-338.

[16]. Ben-Porath, E. (2014). Game Theory, Michael Maschler, Eilon Solan, Shmuel Zamir, Cambridge University Press (2013).

[17]. Durga, M. V. (2016). An efficient algorithm for solving nucleolus of cooperative TU games using MATLAB. Int. J. Innov. Res. Dev, 5.

[18]. Khudaykulova, M., Yuanqiong, H., & Khudaykulov, A. (2022). Economic consequences and implications of the Ukraine-russia war. International Journal of Management Science and Business Administration, 8(4), 44-52.

[19]. Mbah, R. E., & Wasum, D. F. (2022). Russian-Ukraine 2022 War: A review of the economic impact of Russian-Ukraine crisis on the USA, UK, Canada, and Europe. Advances in Social Sciences Research Journal, 9(3), 144-153.

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