Testing the biased geometric Brownian motion - Danswasvong, Thepdanai (2009)
This dissertation proposes a new stock price model “The biased geometric Brownian motion”. In short, the biased geometric Brownian motion is a normal geometric Brownian motion with a newly introduced “biased factor”. The forecasting performance of the biased geometric Brownian motion was tested in order to evaluate whether the efficient portfolio which is constructed from prediction of share prices from this new model will outperforms an optimal portfolio created from the current or past information. The formulation of the biased factor employs the fundamental and principle knowledge on fuzzy logic and fuzzy set theory. Factors which are closely relate to the recent performance of the stock such as the daily rate of return and price movement are described by linguistic variables which are characterised by fuzzy sets. The defuzzification of these variables is the process to calculate the value of the biased factor. In addition to the biased factor, the genetic algorithm was constructed in order to solve the portfolio optimisation problem. The genetic algorithm is used to determine the optimal portfolio in the performance test of the biased geometric Brownian motion. Several tests were conducted in order to verify the performance of the biased geometric Brownian motion and the genetic algorithm. In the end, it turns out that both the original and the biased geometric Brownian motion are unsuitable for the prediction of share price in the current economic recession. On the other hand, the performance of the genetic algorithm in solving the portfolio selection problem was marvellous.