Multi-dimensional geometric Brownian motions, Onsager-Machlup functions, and applications to mathematical finance

Acta Mathematica Scientia

Volumn 20, Issue 3, 2000, Pages 341-358

  Hu, Yaozhong ^a,b  

^a UNIVERSITY OF KANSAS   (United States)

^b Wuhan National Laboratory for Optoelectronics   (China)

Author keywords

Most likely interest rate; Most probable path; Multi dimensional geometric Brownian motions; Onsager Machlup functions; Positivity

Indexed keywords

EID: 0041114373     PISSN: 02529602     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0252-9602(17)30641-0     Document Type: Article

References (28)

1. Arnold V I. Mathematical Methods of Classical Mechanics. Springer-Verlag, 1978
2. Bellman R. Introduction to Matrix Analysis. McGraw-Hill Book Company, INC. 1960
3. Black F, Scholes M. The pricing of options and corporate liabilities. Journal of Political Economy, 1973,81: 637-654
4. Cambanis S, Hu Y Z. The exact convergence rate of Euler-Maruyama scheme and application to sample design. Stochastics and Stochastics Report, 1996, in press
5. Clement E. Correction du bias pour l'estimation d'une diffusion fondée sur une approximation de la vraisemblance. C R Acad Sci Paris, 1996, t322: 281-284
6. Duffie D. State-space models of the term structure of interest rate. Preprint, 1996
7. Duffie D. Security markets : stochastic models. Academic Press, 1988
8. Dacunha-Castelle D, Florens D. Estimation of the coefficient of a diffusion from discrete observations. Stochastics, 1986,19: 263-284
9. Elliott R. Estimating the implicit interest rate of a risky asset. Stochastic Processes Appl, 1994,49: 199-206
10. Fujita T, Kotani S. Onsager-Machlup function for diffusion processes. J Math Kyoto Univ, 1982/83,22: 115-130
11. Goodwin G, Payne R. Dynamic System Identification. Academic Press, 1977
12. Henrici P. Discrete variable methods in ordinary differential equations. New York: Wiley, 1962
13. Hull J C. Options, Futures, and other Derivatives Securities. 2nd edition. Prentice-Hall, INC. 1993
14. Hu Y Z, Øksendal B. Optimal time to invest when the price processes are geometric Brownian motions (Submitted)
15. Hu Y Z. Strong and weak convergence rate of time discretization schemes. In: Azema J, Emery M, Meyer P A, Yor M eds. Séminaire des Prob. XXX. Springer, 1996. 218-227
16. Hu Y, Watanabe S. Donsker delta function and approximation of heat kernel. J Math Kyoto Univ, 1996,36: 499-518
17. Ikeda N, Watanabe S. Stochastic Differential Equations and Diffusion Processes. Second edition. North Holland, 1989
18. Jean W H. The geometric mean and stochastic dominance. Journal of Finance, 1980,35: 151-158
19. Karatzas I, Shreve S. Brownian Motion and Stochastic Calculus. Springer-Verlag, 1988
20. Latané H A. Criteria for choice among risky ventures. Journal of Political Economy, 1959,67: 144-155
21. Kloeden P, Platen E. Numerical Solution of Stochastic Differential Equations. Springer-Verlag, 1992
22. Mayer-Wolf E, Zeitouni O. Onsager-Machlup functionals for non-trace-class SPDEs. Prob Th Rel Fields, 1993,95: 199-216
23. Øksendal B. Stochastic Differential Equations: An Introduction with Applications. Fifth Edition. Springer, 1998
24. Onsager L, Machlup S. Fluctuations and Irreversible processes. I, II, Phys Rev, 1953,91: 1505-1512, 1512-1515
25. Rogers L C G, Satchell S E. Estimating variance from high, low and closing prices. Ann Appl Prob, 1991,1: 504-512
26. Takahashi Y, Watanabe S. The probability functionals (Onsager-Machlup functions) of diffusion processes, In: Stochastic Integral (Proc Sympos Univ Durham, Durham, 1980). Lect Notes in Math, 1981,851: 433-463
27. Vander Weide J H, Peterson D W, Maier S F. Strategy which maximizes the geometric mean return on portfolio investments. Management Science, 1976/77,23: 1117-1123
28. Zeitouni O. On the Onsager-Machlup functional of diffusion processes around non-C2 curves. Ann Prob, 1989, 1037-1054