Skip to main content
Erschienen in: Fuzzy Optimization and Decision Making 2/2019

22.10.2018

European option pricing model based on uncertain fractional differential equation

verfasst von: Ziqiang Lu, Hongyan Yan, Yuanguo Zhu

Erschienen in: Fuzzy Optimization and Decision Making | Ausgabe 2/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, we investigate a new version of stock model under uncertain circumstances for uncertain stock markets. Firstly, solutions to some uncertain fractional differential equations are presented by employing the Mittag-Leffler function. Then, a new uncertain stock model with mean-reverting process is formulated on the basis of uncertain fractional differential equations. Finally, European option pricing formulas based on the proposed model are investigated as well as some numerical examples.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
Zurück zum Zitat Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.MathSciNetMATHCrossRef Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.MathSciNetMATHCrossRef
Zurück zum Zitat Chen, X., & Liu, B. (2010). Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optimization and Decision Making, 9(1), 69–81.MathSciNetMATHCrossRef Chen, X., & Liu, B. (2010). Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optimization and Decision Making, 9(1), 69–81.MathSciNetMATHCrossRef
Zurück zum Zitat Chen, X. (2011). American option pricing formula for uncertain financial market. International Journal of Operations Research, 8(2), 32–37.MathSciNet Chen, X. (2011). American option pricing formula for uncertain financial market. International Journal of Operations Research, 8(2), 32–37.MathSciNet
Zurück zum Zitat Chen, X., Liu, Y., & Ralescu, D. A. (2013). Uncertain stock model with periodic dividends. Fuzzy Optimization and Decision Making, 12(1), 111–123.MathSciNetMATHCrossRef Chen, X., Liu, Y., & Ralescu, D. A. (2013). Uncertain stock model with periodic dividends. Fuzzy Optimization and Decision Making, 12(1), 111–123.MathSciNetMATHCrossRef
Zurück zum Zitat Chen, X., & Park, G. K. (2014). Uncertain expected utility function and its risk premium. Journal of Intelligent Manufacturing, 28(3), 581–587.CrossRef Chen, X., & Park, G. K. (2014). Uncertain expected utility function and its risk premium. Journal of Intelligent Manufacturing, 28(3), 581–587.CrossRef
Zurück zum Zitat Ji, X., & Ke, H. (2017). No-arbitrage theorem for multi-factor uncertain stock model with floating interest rate. Fuzzy Optimization and Decision Making, 16(2), 221–234.MathSciNetMATHCrossRef Ji, X., & Ke, H. (2017). No-arbitrage theorem for multi-factor uncertain stock model with floating interest rate. Fuzzy Optimization and Decision Making, 16(2), 221–234.MathSciNetMATHCrossRef
Zurück zum Zitat Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and application of fractional differential equation. Amsterdam: Elsevier.MATH Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and application of fractional differential equation. Amsterdam: Elsevier.MATH
Zurück zum Zitat Li, B., Zhu, Y., Sun, Y., Aw, Grace, & Teo, K. L. (2018). Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint. Applied Mathematical Modelling, 56, 539–550.MathSciNetCrossRef Li, B., Zhu, Y., Sun, Y., Aw, Grace, & Teo, K. L. (2018). Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint. Applied Mathematical Modelling, 56, 539–550.MathSciNetCrossRef
Zurück zum Zitat Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.MATH Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.MATH
Zurück zum Zitat Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems, 2(1), 3–16. Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems, 2(1), 3–16.
Zurück zum Zitat Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10. Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.
Zurück zum Zitat Liu, B. (2013). Toward uncertain finance theory. Journal of Uncertainty Analysis and Applications, 1(1), 1–15.CrossRef Liu, B. (2013). Toward uncertain finance theory. Journal of Uncertainty Analysis and Applications, 1(1), 1–15.CrossRef
Zurück zum Zitat Liu, H., Ke, H., & Fei, W. (2014). Almost sure stability for uncertain differential equation. Fuzzy Optimization and Decision Making, 13(4), 463–473.MathSciNetMATHCrossRef Liu, H., Ke, H., & Fei, W. (2014). Almost sure stability for uncertain differential equation. Fuzzy Optimization and Decision Making, 13(4), 463–473.MathSciNetMATHCrossRef
Zurück zum Zitat Podlubny, I. (1999). Fractional differential equation. San Diego: Academic Press.MATH Podlubny, I. (1999). Fractional differential equation. San Diego: Academic Press.MATH
Zurück zum Zitat Peng, J., & Yao, K. (2011). A new option pricing model for stocks in uncertainty markets. International Journal of Operations Research, 8(2), 18–26.MathSciNet Peng, J., & Yao, K. (2011). A new option pricing model for stocks in uncertainty markets. International Journal of Operations Research, 8(2), 18–26.MathSciNet
Zurück zum Zitat Sun, J., & Chen, X. (2015). Asian option pricing formula for uncertain financial market. Journal of Uncertainty Analysis and Applications, 3(11), 1–11. Sun, J., & Chen, X. (2015). Asian option pricing formula for uncertain financial market. Journal of Uncertainty Analysis and Applications, 3(11), 1–11.
Zurück zum Zitat Sun, Y., & Su, T. (2017). Mean-reverting stock model with floating interest rate in uncertain environment. Fuzzy Optimization and Decision Making, 16(2), 235–255.MathSciNetMATHCrossRef Sun, Y., & Su, T. (2017). Mean-reverting stock model with floating interest rate in uncertain environment. Fuzzy Optimization and Decision Making, 16(2), 235–255.MathSciNetMATHCrossRef
Zurück zum Zitat Tao, N., & Zhu, Y. (2015). Attractivity and stability analysis of uncertain differential systems. International Journal of Bifurcation and Chaos, 25(2), 1550022-1–1550022-10. Tao, N., & Zhu, Y. (2015). Attractivity and stability analysis of uncertain differential systems. International Journal of Bifurcation and Chaos, 25(2), 1550022-1–1550022-10.
Zurück zum Zitat Yao, K., & Chen, X. (2013). A numerical method for solving uncertain differential equations. Journal of Intelligent and Fuzzy Systems, 25, 825–832.MathSciNetMATHCrossRef Yao, K., & Chen, X. (2013). A numerical method for solving uncertain differential equations. Journal of Intelligent and Fuzzy Systems, 25, 825–832.MathSciNetMATHCrossRef
Zurück zum Zitat Yao, K., Ke, H., & Sheng, Y. (2015). Stability in mean for uncertain differential equation. Fuzzy Optimization and Decision Making, 14(3), 365–379.MathSciNetMATHCrossRef Yao, K., Ke, H., & Sheng, Y. (2015). Stability in mean for uncertain differential equation. Fuzzy Optimization and Decision Making, 14(3), 365–379.MathSciNetMATHCrossRef
Zurück zum Zitat Yao, K. (2015). Uncertain contour process and its application in stock model with floating interest rate. Fuzzy Optimization and Decision Making, 14(4), 399–424.MathSciNetMATHCrossRef Yao, K. (2015). Uncertain contour process and its application in stock model with floating interest rate. Fuzzy Optimization and Decision Making, 14(4), 399–424.MathSciNetMATHCrossRef
Zurück zum Zitat Zhu, Y. (2010). Uncertain optimal control with application to a portfolio selection model. Cybernetics and Systems: An International Journal, 41(7), 535–547.MATHCrossRef Zhu, Y. (2010). Uncertain optimal control with application to a portfolio selection model. Cybernetics and Systems: An International Journal, 41(7), 535–547.MATHCrossRef
Zurück zum Zitat Zhu, Y. (2015a). Uncertain fractional differential equations and an interest rate model. Mathematical Methods in the Applied Sciences, 38(15), 3359–3368.MathSciNetMATHCrossRef Zhu, Y. (2015a). Uncertain fractional differential equations and an interest rate model. Mathematical Methods in the Applied Sciences, 38(15), 3359–3368.MathSciNetMATHCrossRef
Zurück zum Zitat Zhu, Y. (2015b). Exitence and uniquence of the solution to uncertain fractional differential equation. Journal of Uncertainty Analysis and Appliations, 3(5), 1–11. Zhu, Y. (2015b). Exitence and uniquence of the solution to uncertain fractional differential equation. Journal of Uncertainty Analysis and Appliations, 3(5), 1–11.
Metadaten
Titel
European option pricing model based on uncertain fractional differential equation
verfasst von
Ziqiang Lu
Hongyan Yan
Yuanguo Zhu
Publikationsdatum
22.10.2018
Verlag
Springer US
Erschienen in
Fuzzy Optimization and Decision Making / Ausgabe 2/2019
Print ISSN: 1568-4539
Elektronische ISSN: 1573-2908
DOI
https://doi.org/10.1007/s10700-018-9293-4

Weitere Artikel der Ausgabe 2/2019

Fuzzy Optimization and Decision Making 2/2019 Zur Ausgabe