Linear filtering of systems with memory and application to finance

Journal of Applied Mathematics and Stochastic Analysis

Volumn 2006, Issue , 2006, Pages

  Inoue, A ^a   Nakano, Y ^b   Anh, V ^c  

^a HOKKAIDO UNIVERSITY   (Japan)

^b OSAKA UNIVERSITY   (Japan)

^c QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645694358     PISSN: 10489533     EISSN: 16872177     Source Type: Journal    
DOI: 10.1155/JAMSA/2006/53104     Document Type: Article

References (21)

1. V. V. Anh A. Inoue Financial markets with memory. I. Dynamic models Stochastic Analysis and Applications Stochastic Analysis and Applications 23 2005 2 275-300
2. V. V. Anh A. Inoue Y. Kasahara Financial markets with memory. II. Innovation processes and expected utility maximization Stochastic Analysis and Applications Stochastic Analysis and Applications 23 2005 2 301-328
3. V. V. Anh A. Inoue C. Pesee Incorporation of memory into the Black-Scholes-Merton theory and estimation of volatility submitted. Available at http://www.math.hokudai.ac.jp/~inoue/
4. R. S. Bucy P. D. Joseph Filtering for Stochastic Processes with Applications to Guidance Interscience Tracts in Pure and Applied Mathematics, no. 23 InterScience New York 1968 xviii+195
5. M. H. A. Davis Linear Estimation and Stochastic Control Chapman and Hall Mathematics Series Chapman and Hall London 1977 xii+224
6. J. B. Detemple Asset pricing in a production economy with incomplete information The Journal of Finance 41 1986 2 383-391
7. D. Feldman M. U. Dothan Equilibrium interest rates and multiperiod bonds in a partially observable economy The Journal of Finance 41 1986 2 369-382
8. G. Gennotte Optimal portfolio choice under incomplete information The Journal of Finance 41 1986 3 733-746
9. G. Gripenberg S.-O. Londen O. Staffans Volterra Integral and Functional Equations Encyclopedia of Mathematics and Its Applications 34 Cambridge University Press Cambridge 1990 xxii+701
10. A. Inoue Y. Nakano V. V. Anh Binary market models with memory submitted. Available at http://www.math.hokudai.ac.jp/~inoue/
11. A. H. Jazwinski Stochastic Processes and Filtering Theory Academic Press New York 1970
12. R. E. Kalman A new approach to linear filtering and prediction problems Transactions of the ASME. Series D: Journal of Basic Engineering 82 1960 35-45
13. R. E. Kalman R. S. Bucy New results in linear filtering and prediction theory Transactions of the ASME. Series D: Journal of Basic Engineering 83 1961 95-108
14. I. Karatzas S. E. Shreve Methods of Mathematical Finance Applications of Mathematics 39 Springer New York 1998 xvi+407
15. I. Karatzas X. Zhao Bayesian adaptive portfolio optimization Option Pricing, Interest Rates and Risk Management Handb. Math. Finance Cambridge University Press Cambridge 2001 632-669
16. M. L. Kleptsyna P. E. Kloeden V. V. Anh Linear filtering with fractional Brownian motion Stochastic Analysis and Applications Stochastic Analysis and Applications 16 1998 5 907-914
17. M. L. Kleptsyna A. Le Breton Extension of the Kalman-Bucy filter to elementary linear systems with fractional Brownian noises Statistical Inference for Stochastic Processes. An International Journal Devoted to Time Series Analysis and the Statistics of Continuous Time Processes and Dynamical Systems Statistical Inference for Stochastic Processes. An International Journal Devoted to Time Series Analysis and the Statistics of Continuous Time Processes and Dynamical Systems 5 2002 3 249-271
18. M. L. Kleptsyna A. Le Breton M.-C. Roubaud General approach to filtering with fractional Brownian noises - Application to linear systems Stochastics and Stochastics Reports Stochastics and Stochastics Reports 71 2000 1-2 119-140 119-140
19. P. Lakner Utility maximization with partial information Stochastic Processes and their Applications Stochastic Processes and their Applications 56 1995 2 247-273
20. P. Lakner Optimal trading strategy for an investor: The case of partial information Stochastic Processes and their Applications Stochastic Processes and their Applications 76 1998 1 77-97
21. R. S. Liptser A. N. Shiryaev Statistics of Random Processes. I. General Theory Applications of Mathematics 5 Springer Berlin 2nd 2001 xvi+427