Mathematical modeling of asset price dynamics in the markets involving homugeneous groups

In this thesis, a new mathematical model which is derived by using a new relative price change formula is introduced for estimating asset price changes. In this model, a system is considered which has some assumptions valid in practice, contrary to the assumptions of classical economics which are not useful in practice and the system consists of a single asset and a homogeneous group of investors. The single asset in the system is traded by investors in the system. At first, the system is considered as a conserved system and then it is extended to system which involves exogenous cash and shares. Asset price diynamics is studied with this mathematical model in a market involving more information on demand and supply for a stock rather than their values at a price.The basis of the mathematical model grounds on the studies which are based on the fundamental principal of classical economy ?an equilibrium price is attained when supply and demand are equal?. However in this thesis differently from the previous studies, a new relative price change formula derived by Caginalp is used instead of the relative price change formula involves excess demand function. This formula includes not only the values at a price but also first derivatives of demand and supply functions. The mathematical model derived by using this new formula may yield a better forecast than the formula involves excess demand function in markets involving more information about demand and supply functions.Keywords: Asset price dynamics, equilibrium point, nonlinear demand and supply functions.