A stock model with jumps for uncertain markets

International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems

Volumn 20, Issue 3, 2012, Pages 421-432

  Yu, Xichang ^a  

^a Liaocheng Vocational and Technical College   (China)

Author keywords

European option; Stock model; Uncertain differential equation with jumps; Uncertain finance

Indexed keywords

COMMERCE; DIFFERENTIAL EQUATIONS;

CANONICAL PROCESS; EUROPEAN OPTION; PUT OPTIONS; RENEWAL PROCESS; STOCK MODELS; UNCERTAIN DIFFERENTIAL EQUATION WITH JUMP; UNCERTAIN DIFFERENTIAL EQUATIONS; UNCERTAIN FINANCE; UNCERTAIN MARKETS; UNCERTAIN PROCESS;

FINANCIAL MARKETS;

EID: 84862085939     PISSN: 02184885     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218488512500213     Document Type: Article

References (20)

1. L. Bachelier, Th́eorie de la sṕeculation, Annales scientifiques de l'́ Ecole normale suṕerieure 17 (1900) 21-86.
2. F. Black and P. Karasinski, Bond and option pricing when short-term rates are lognormal, Financial Analysts J. 4 (1991) 52-59.
3. F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Political Economy 81 (1973) 637-654.
4. X. Chen and B. Liu, Existence and uniqueness theorem for uncertain differential equations, Fuzzy Optimization and Decision Making 1 (2010) 69-81.
5. X. Chen, American option pricing formula for uncertain financial market, Int. J. Operations Research 2 (2011) 32-37.
6. X. Gao, Some properties of continuous uncertain measure, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 3 (2009) 419-426.
7. J. Hull and A. White, Pricing interest rate derivative securities, Review of Financial Studies 3 (1990) 573-592.
8. L. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus (Springer-Verlag, New York, 1991).
9. L. Karatzas and S. Shreve, Methods of Mathematical Finance (Springer-Verlag, New York, 1998).
10. B. Liu, Uncertainty Theory, 2nd edn. (Springer-Verlag, Berlin, 2007).
11. B. Liu, Fuzzy process, hybrid process and uncertain process, J. Uncertain Systems 1 (2008) 3-16.
12. B. Liu, Some research problems in uncertainty theory, J. Uncertain Systems 1 (2009) 3-10.
13. B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty (Springer-Verlag, Berlin, 2010).
14. Y. Liu, and X. Chen, Uncertain currency model and currency option pricing, http://orsc.edu.cn/online/091010.pdf.
15. R. Merton, Theory of rational option pricing, Bell J. Economics & Management Science, 1 (1973) 141-183.
16. J. Peng and K. Yao, A new option pricing model for stocks in uncertainty markets, Int. J. Operations Research 2 (2011) 18-26.
17. P. Samuelson, Proof that properly anticipated prices fluctuate randomly, Industrial Management Review 6 (1965) 41-50.
18. P. Samuelson, Mathematics of speculative prices, Siam Review 15 (1973) 1-42.
19. K. Yao, Uncertain calculus with renewal process, Fuzzy Optimization and Decision Making, to be published.
20. C. You, Some convergence theorems of uncertain sequences, Mathematical and Computer Modelling 3-4 (2009) 482-487.