Approach of Riemann-Stieltjes Integral to the Function of the Fractional Brownian Motion

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Abstract

By : Sherly Octavia Bouk

Email : sherlybouk@gmail.com

Faculties : Fakultas Matematika dan Ilmu Pengetahuan Alam

Department : S1 Matematika

Riemann-Stieltjes Integral is a common form of the Riemann integral by taking integrator the form of a continuous function with limited variation. In the financial field, the data rate of return on stocks in investment activity is continuous so that the Fractional Brownian Motion model can be used to determine the value of the stock index, one of them in investment activity in the IHSG. Based on the results of model simulations, the function of Fractional Brownian Motion to , provide a lower value than the value of the simulation using Brownian motion function, where . If the parameter value reduced to , then the simulation results of Fractional Brownian Motion function would resemble ordinary Brownian motion function.

Keyword : Riemann-Stieltjes Integral, Fractional Brownian Motion, the value of stock index

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