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Nonparametric identification method of stochastic differential equation with fractal Brownian motion

Filatova D., Grzywaczewski M.

Journal of Automation Mobile Robotics and Intelligent Systems

2007

Vol. 1, No. 2

45-49

This Paper presents a methodology for estimating the parameters of stochastic differential equation (SDE) driven by froctional Brownian motion (fBm). The main idea is connected with simulated maximum likelihood.To develop the methodology, two iimportant questions, namely how to generote fBm sample paths with different values of the Hurst parameter and how to estimate Hurst parometer are studied. Aa Effectiveness of the methodology is analyzed through Monte Carlo simulations.

Numerical solution of portfolio optimal control with constraints: the case of the object as weakly singular integral equation

Filatova D., Grzywaczewski M.

Journal of Applied Computer Science

2007

Vol. 15, nr 2

51-69

We consider the model of optimal portfolio of Mertons’ market model. The noises involved in the dynamics of the wealth are fractional white noises. The stochastic optimal control problem is converted into a non-random optimization. An example of problem numerical solution illustrates proposed methodology.