American Institute of Mathematical Sciences

• Previous Article
Perturbation analysis of a class of conic programming problems under Jacobian uniqueness conditions
• JIMO Home
• This Issue
• Next Article
Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework
doi: 10.3934/jimo.2018158

Option pricing formulas for generalized fuzzy stock model

 College of Mathematics and Information Science, Hebei University, Baoding 071002, China

* Corresponding author: Cuilian You

Received  June 2018 Revised  June 2018 Published  September 2018

Fund Project: The first author is supported by NSFC grant (No.61773150) and Key Lab. of Machine Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding, 071002, China

Fuzzy stock model has been studied by many scholars in recent years, in which option pricing problem is the most important part. In this paper, we studied option pricing for a new generalized fuzzy stock model. Based on credibility theory, pricing formulas of European option and American option were obtained.

Citation: Cuilian You, Le Bo. Option pricing formulas for generalized fuzzy stock model. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018158
References:
 [1] F. Black and M. Scholes, The pricing of option and corporate liabilities, Journal of Political Economy, 81 (1973), 637-654. doi: 10.1086/260062. [2] X. Chen and Z. Qin, A new existence and uniqueness theorem for fuzzy differential equation, International Journal of Fuzzy Systems, 13 (2011), 148-151. [3] W. Dai, Reflection principle of Liu process, 2007. Available from: http://orsc.edu.cn/process\/071110.pdf. [4] W. Dai, Lipschitz continuity of Liu process, 2008. Available from: http://orsc.edu.cn/process\/080831.pdf. [5] Z. Ding, M. Ma and A. Kandel, Exsitence of the solutions of fuzzy differential equations with parameters, Information Sciences, 99 (1999), 205-217. doi: 10.1016/S0020-0255(96)00279-4. [6] J. Gao and X. Gao, A new stock model for credibilistic option pricing, Journal of Uncertain Systems, 2 (2008), 243-247. [7] X. Gao and X. Chen, Option pricing formula for generalized stock models, 2008. Available from: http://orsc.edu.cn/process/080317.pdf. [8] H. Hu, Power option pricing model for stock price follow geometric fractional Liu process, Journal of Henan Normal University (Natural Science Edition), 41 (2013), 1-5. [9] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24 (1987), 301-317. doi: 10.1016/0165-0114(87)90029-7. [10] B. Liu, Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems, 2 (2008), 3-16. [11] B. Liu and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems, 10 (2002), 445-450. [12] R. Merton, Theory of rational option pricing, Bell Journal of Economics and Management Science, 4 (1973), 141-183. doi: 10.2307/3003143. [13] J. Peng, A general stock model for fuzzy markets, Journal of Uncertain Systems, 2 (2008), 248-254. [14] Z. Qin and X. Li, Option pricing formula for fuzzy financial market, Journal of Uncertain System, 2 (2008), 17-21. [15] Z. Qin and X. Li, Fuzzy calculus for finance, 2008. Available from: http://orsc.edu.cn/process\/fc.pdf. [16] C. You, H. Huo and W. Wang, Multi-dimensional Liu process, differential and integral, East Asian Mathematical Journal, 29 (2013), 13-22. doi: 10.7858/eamj.2013.002. [17] C. You, H. Ma and H. Huo, A new kind of generalized fuzzy integrals, Journal of Nonlinear Science and Applications, 9 (2016), 1396-1401. doi: 10.22436/jnsa.009.03.63. [18] C. You and G. Wang, Properties of a new kind of fuzzy integral, Journal of Hebei University (Natural Science Edition), 31 (2011), 337-340. [19] C. You, W. Wang and H. Huo, Existence and unqiueness theorems for fuzzy differential equation, Journal of Uncertain Systems, 7 (2013), 303-315. [20] L. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X.

show all references

References:
 [1] F. Black and M. Scholes, The pricing of option and corporate liabilities, Journal of Political Economy, 81 (1973), 637-654. doi: 10.1086/260062. [2] X. Chen and Z. Qin, A new existence and uniqueness theorem for fuzzy differential equation, International Journal of Fuzzy Systems, 13 (2011), 148-151. [3] W. Dai, Reflection principle of Liu process, 2007. Available from: http://orsc.edu.cn/process\/071110.pdf. [4] W. Dai, Lipschitz continuity of Liu process, 2008. Available from: http://orsc.edu.cn/process\/080831.pdf. [5] Z. Ding, M. Ma and A. Kandel, Exsitence of the solutions of fuzzy differential equations with parameters, Information Sciences, 99 (1999), 205-217. doi: 10.1016/S0020-0255(96)00279-4. [6] J. Gao and X. Gao, A new stock model for credibilistic option pricing, Journal of Uncertain Systems, 2 (2008), 243-247. [7] X. Gao and X. Chen, Option pricing formula for generalized stock models, 2008. Available from: http://orsc.edu.cn/process/080317.pdf. [8] H. Hu, Power option pricing model for stock price follow geometric fractional Liu process, Journal of Henan Normal University (Natural Science Edition), 41 (2013), 1-5. [9] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24 (1987), 301-317. doi: 10.1016/0165-0114(87)90029-7. [10] B. Liu, Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems, 2 (2008), 3-16. [11] B. Liu and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems, 10 (2002), 445-450. [12] R. Merton, Theory of rational option pricing, Bell Journal of Economics and Management Science, 4 (1973), 141-183. doi: 10.2307/3003143. [13] J. Peng, A general stock model for fuzzy markets, Journal of Uncertain Systems, 2 (2008), 248-254. [14] Z. Qin and X. Li, Option pricing formula for fuzzy financial market, Journal of Uncertain System, 2 (2008), 17-21. [15] Z. Qin and X. Li, Fuzzy calculus for finance, 2008. Available from: http://orsc.edu.cn/process\/fc.pdf. [16] C. You, H. Huo and W. Wang, Multi-dimensional Liu process, differential and integral, East Asian Mathematical Journal, 29 (2013), 13-22. doi: 10.7858/eamj.2013.002. [17] C. You, H. Ma and H. Huo, A new kind of generalized fuzzy integrals, Journal of Nonlinear Science and Applications, 9 (2016), 1396-1401. doi: 10.22436/jnsa.009.03.63. [18] C. You and G. Wang, Properties of a new kind of fuzzy integral, Journal of Hebei University (Natural Science Edition), 31 (2011), 337-340. [19] C. You, W. Wang and H. Huo, Existence and unqiueness theorems for fuzzy differential equation, Journal of Uncertain Systems, 7 (2013), 303-315. [20] L. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X.
 [1] Cuilian You, Yangyang Hao. Stability in mean for fuzzy differential equation. Journal of Industrial & Management Optimization, 2018, 13 (5) : 1-11. doi: 10.3934/jimo.2018099 [2] Natalia Skripnik. Averaging of fuzzy integral equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1999-2010. doi: 10.3934/dcdsb.2017118 [3] Xiao-Qian Jiang, Lun-Chuan Zhang. A pricing option approach based on backward stochastic differential equation theory. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 969-978. doi: 10.3934/dcdss.2019065 [4] Andrej V. Plotnikov, Tatyana A. Komleva, Liliya I. Plotnikova. The averaging of fuzzy hyperbolic differential inclusions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1987-1998. doi: 10.3934/dcdsb.2017117 [5] Lisha Wang, Huaming Song, Ding Zhang, Hui Yang. Pricing decisions for complementary products in a fuzzy dual-channel supply chain. Journal of Industrial & Management Optimization, 2019, 15 (1) : 343-364. doi: 10.3934/jimo.2018046 [6] Feyza Gürbüz, Panos M. Pardalos. A decision making process application for the slurry production in ceramics via fuzzy cluster and data mining. Journal of Industrial & Management Optimization, 2012, 8 (2) : 285-297. doi: 10.3934/jimo.2012.8.285 [7] Dariush Mohamadi Zanjirani, Majid Esmaelian. An integrated approach based on Fuzzy Inference System for scheduling and process planning through multiple objectives. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-25. doi: 10.3934/jimo.2018202 [8] Xiaodong Liu, Wanquan Liu. The framework of axiomatics fuzzy sets based fuzzy classifiers. Journal of Industrial & Management Optimization, 2008, 4 (3) : 581-609. doi: 10.3934/jimo.2008.4.581 [9] Jiaquan Zhan, Fanyong Meng. Cores and optimal fuzzy communication structures of fuzzy games. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 1187-1198. doi: 10.3934/dcdss.2019082 [10] Juan J. Nieto, M. Victoria Otero-Espinar, Rosana Rodríguez-López. Dynamics of the fuzzy logistic family. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 699-717. doi: 10.3934/dcdsb.2010.14.699 [11] Purnima Pandit. Fuzzy system of linear equations. Conference Publications, 2013, 2013 (special) : 619-627. doi: 10.3934/proc.2013.2013.619 [12] Harish Garg. Some robust improved geometric aggregation operators under interval-valued intuitionistic fuzzy environment for multi-criteria decision-making process. Journal of Industrial & Management Optimization, 2018, 14 (1) : 283-308. doi: 10.3934/jimo.2017047 [13] Erik Kropat, Gerhard Wilhelm Weber. Fuzzy target-environment networks and fuzzy-regression approaches. Numerical Algebra, Control & Optimization, 2018, 8 (2) : 135-155. doi: 10.3934/naco.2018008 [14] Wei Wang, Xiao-Long Xin. On fuzzy filters of Heyting-algebras. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1611-1619. doi: 10.3934/dcdss.2011.4.1611 [15] Tayel Dabbous. Adaptive control of nonlinear systems using fuzzy systems. Journal of Industrial & Management Optimization, 2010, 6 (4) : 861-880. doi: 10.3934/jimo.2010.6.861 [16] Guojun Gan, Qiujun Lan, Shiyang Sima. Scalable clustering by truncated fuzzy $c$-means. Big Data & Information Analytics, 2016, 1 (2&3) : 247-259. doi: 10.3934/bdia.2016007 [17] Gang Chen, Zaiming Liu, Jingchuan Zhang. Analysis of strategic customer behavior in fuzzy queueing systems. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-16. doi: 10.3934/jimo.2018157 [18] Farid Tari. Geometric properties of the integral curves of an implicit differential equation. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 349-364. doi: 10.3934/dcds.2007.17.349 [19] Shaokuan Chen, Shanjian Tang. Semi-linear backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. Mathematical Control & Related Fields, 2015, 5 (3) : 401-434. doi: 10.3934/mcrf.2015.5.401 [20] Lukáš Adam, Jiří Outrata. On optimal control of a sweeping process coupled with an ordinary differential equation. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 2709-2738. doi: 10.3934/dcdsb.2014.19.2709

2017 Impact Factor: 0.994