scholarly journals Mathematical Model of Stock Prices via a Fractional Brownian Motion Model with Adaptive Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Tidarut Areerak
Keyword(s):  
Mathematical Model ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stock Prices ◽  
Motion Model ◽  
Adaptive Parameters ◽  
Company Limited ◽  
Public Company ◽  
Proposed Model ◽  
Brownian Motion Model

The paper presents a mathematical model of stock prices using a fractional Brownian motion model with adaptive parameters (FBMAP). The accuracy index of the proposed model is compared with the Brownian motion model with adaptive parameters (BMAP). The parameters in both models are adapted at any time. The ADVANC Info Service Public Company Limited (ADVANC) and Land and Houses Public Company Limited (LH) closed prices are concerned in the paper. The Brownian motion model with adaptive parameters (BMAP) and fractional Brownian motion model with adaptive parameters (FBMAP) are applied to identify ADVANC and LH closed prices. The simulation results show that the FBMAP is more suitable for forecasting the ADVANC and LH closed price than the BMAP.

Pricing Model for Convertible Bonds: A Mixed Fractional Brownian Motion with Jumps

2015 ◽  
Vol 5 (3) ◽  
pp. 222-237 ◽  
Author(s):  
Jie Miao ◽  
Xu Yang
Keyword(s):  
Mathematical Model ◽  
Brownian Motion ◽  
Empirical Study ◽  
Fractional Brownian Motion ◽  
Conditional Expectation ◽  
Convertible Bonds ◽  
Motion Model ◽  
Pricing Model ◽  
Mixed Fractional Brownian Motion ◽  
Brownian Motion Model

AbstractA mathematical model to price convertible bonds involving mixed fractional Brownian motion with jumps is presented. We obtain a general pricing formula using the risk neutral pricing principle and quasi-conditional expectation. The sensitivity of the price to changing various parameters is discussed. Theoretical prices from our jump mixed fractional Brownian motion model are compared with the prices predicted by traditional models. An empirical study shows that our new model is more acceptable.

scholarly journals The voice of Physics in finance: A glance on the theoretical application of heat equation to stock price diffusions

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Leonard Mushunje
Keyword(s):  
Brownian Motion ◽  
Heat Equation ◽  
Stock Prices ◽  
Stock Price ◽  
Price Volatility ◽  
Heat Diffusion ◽  
Motion Model ◽  
Asset Valuation ◽  
Brownian Motion Model ◽  
Theoretical Application

Stock price volatility is considered the main matter of concern within the investment grounds. However, the diffusivity of these prices should as well be considered. As such, proper modelling should be done for investors to stay healthy-informed. This paper suggest to model stock price diffusions using the heat equation from physics. We hypothetically state that, our model captures and model the diffusion bubbles of stock prices with a better precision of reality. We compared our model with the standard geometric Brownian motion model which is the wide commonly used stochastic differential equation in asset valuation. Interestingly, the models proved to agree as evidenced by a bijective relation between the volatility coefficients of the Brownian motion model and the diffusion coefficients of our heat diffusion model as well as the corresponding drift components. Consequently, a short proof for the martingale of our model is done which happen to hold. 

scholarly journals Stochastic Fractal Dimension Image

2009 ◽  
Author(s):  
Nicholas J. Tustison ◽  
James Gee
Keyword(s):  
Brownian Motion ◽  
Fractal Dimension ◽  
Fractional Brownian Motion ◽  
Fractal Analysis ◽  
Medical Image ◽  
Fractal Theory ◽  
Motion Model ◽  
Edge Enhancement ◽  
Brownian Motion Model ◽  
Medical Image Classification

Fractal analysis for medical image classification and analysis was introduced in cite{Chen1989}. According to the authors, when viewed as an intensity surface, Mandelbrot's fractal theory provides an informative framework for characterizing such a surface. Using the fractional Brownian motion model, the authors provide an algorithm for converting a scalar image to a fractal dimension image for classification purposes or edge enhancement. This submission constitutes a report on the ITK implementation of this algorithm.

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