Mathematical modeling and stability analyses of financial markets involving two assets and one trading group

In this thesis, we present a mathematical model for a market involving two stocks which are traded within a single homogeneous group of investors who have a similar motivations and strategies for trading. It is assumed that the market consists of a fixed amount of cash and stocks, and that the trading group is affected by trend and valuation motivations while selling or buying each asset, but follows a strategy in which the buying of an asset depends on the other asset's price while the selling does not. By utilizing these assumptions and basic microeconomics principles, the mathematical model is obtained through a dynamical system approach. We analyse the stability of equilibrium points of the model when the trading group follows a value based strategy for each stocks, and determine the conditions on parameters for stability. For systems in which the group attaches importance to the valuation of one stock and the trend of other stock for trading, we establish conditions for stability. We form an example for the model defined in the former section by taking appropriate functions for the transition rate functions. We prove that if the group of traders focuses on only fundamental values of each stock, then all equilibria are stable. We establish conditions for stability of system in which the trading group follows a mixed treading strategy, i.e., they follow a pure value-based strategy while selling or buying the first asset, and a pure trend-based strategy while selling or buying the second asset. Moreover, we argue the existence of periodic solutions through a Hopf bifurcation by choosing the momentum coefficient as a bifurcation parameter within this setting. Finally, we give examples and numerical simulations to support and extend the analytical results.