Abstract
We study the linear filtering problem for systems driven by
continuous Gaussian processes
We study the linear filtering problem for systems driven by
continuous Gaussian processes
V. V. Anh and A. Inoue, “Financial markets with memory. I. Dynamic models,” Stochastic Analysis and Applications, vol. 23, no. 2, pp. 275–300, 2005.
View at: Google Scholar | MathSciNetV. V. Anh, A. Inoue, and Y. Kasahara, “Financial markets with memory. II. Innovation processes and expected utility maximization,” Stochastic Analysis and Applications, vol. 23, no. 2, pp. 301–328, 2005.
View at: Google Scholar | MathSciNetV. V. Anh, A. Inoue, and 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/.
View at: Google ScholarR. S. Bucy and P. D. Joseph, Filtering for Stochastic Processes with Applications to Guidance, Interscience Tracts in Pure and Applied Mathematics, no. 23, InterScience, New York, 1968.
View at: Zentralblatt MATH | MathSciNetM. H. A. Davis, Linear Estimation and Stochastic Control, Chapman and Hall Mathematics Series, Chapman & Hall, London, 1977.
View at: Zentralblatt MATH | MathSciNetJ. B. Detemple, “Asset pricing in a production economy with incomplete information,” The Journal of Finance, vol. 41, no. 2, pp. 383–391, 1986.
View at: Google ScholarD. Feldman and M. U. Dothan, “Equilibrium interest rates and multiperiod bonds in a partially observable economy,” The Journal of Finance, vol. 41, no. 2, pp. 369–382, 1986.
View at: Google ScholarG. Gennotte, “Optimal portfolio choice under incomplete information,” The Journal of Finance, vol. 41, no. 3, pp. 733–746, 1986.
View at: Google ScholarG. Gripenberg, S.-O. Londen, and O. Staffans, Volterra Integral and Functional Equations, vol. 34 of Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 1990.
View at: Zentralblatt MATH | MathSciNetA. Inoue, Y. Nakano, and V. V. Anh, “Binary market models with memory,” submitted. Available at http://www.math.hokudai.ac.jp/~inoue/.
View at: Google ScholarA. H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, New York, 1970.
View at: Zentralblatt MATHR. E. Kalman, “A new approach to linear filtering and prediction problems,” Transactions of the ASME. Series D: Journal of Basic Engineering, vol. 82, pp. 35–45, 1960.
View at: Google ScholarR. E. Kalman and R. S. Bucy, “New results in linear filtering and prediction theory,” Transactions of the ASME. Series D: Journal of Basic Engineering, vol. 83, pp. 95–108, 1961.
View at: Google Scholar | MathSciNetI. Karatzas and S. E. Shreve, Methods of Mathematical Finance, vol. 39 of Applications of Mathematics, Springer, New York, 1998.
View at: Zentralblatt MATH | MathSciNetI. Karatzas and X. Zhao, “Bayesian adaptive portfolio optimization,” in Option Pricing, Interest Rates and Risk Management, Handb. Math. Finance, pp. 632–669, Cambridge University Press, Cambridge, 2001.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. L. Kleptsyna, P. E. Kloeden, and V. V. Anh, “Linear filtering with fractional Brownian motion,” Stochastic Analysis and Applications, vol. 16, no. 5, pp. 907–914, 1998.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. L. Kleptsyna and 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, vol. 5, no. 3, pp. 249–271, 2002.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. L. Kleptsyna, A. Le Breton, and M.-C. Roubaud, “General approach to filtering with fractional Brownian noises—application to linear systems,” Stochastics and Stochastics Reports, vol. 71, no. 1-2, pp. 119–140, 2000.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. Lakner, “Utility maximization with partial information,” Stochastic Processes and their Applications, vol. 56, no. 2, pp. 247–273, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. Lakner, “Optimal trading strategy for an investor: the case of partial information,” Stochastic Processes and their Applications, vol. 76, no. 1, pp. 77–97, 1998.
View at: Google Scholar | Zentralblatt MATH | MathSciNetR. S. Liptser and A. N. Shiryaev, Statistics of Random Processes. I. General Theory, vol. 5 of Applications of Mathematics, Springer, Berlin, 2nd edition, 2001.
View at: Zentralblatt MATH | MathSciNet