Nonlinear Dynamical Pricing Models With Heterogeneous Agents And Its Applications

Nearly twenty years, the global economic and financial episodes lead to significant price fluctuations. The researchs about dynamical pricing models of variables and its applications have more important theoretical value and practical significance for the related policy development of governors.By combining heterogeneous agent models,simulation experiments and(or) empirical tests, this paper investigates dynamics and(or) stability of variables which include stock prices, exchange rates,inflation rates and so on. Moreover, the policy implications of the findings are all provided. The main distinctive research work and conclusions are as follows:Firstly,after constructing a two-dimensional nonlinear dynamical model of security prices under the"T+1"trading mechanism of the China's stock market, we analyze the evolution and stability of assets prices when the transition probabilities between buyers and sellers can be influenced by the heterogeneous speed of opinion change, trading strategy of the mean reversion and the contagion effect. Moreover,we use empirical test to study these factors of the transition probabilities in the China's stock market. It is shown that the heterogeneous speed of opinion change between buyers and sellers cause the equilibrium price deviating from fundamental value, and assets prices gradually exhibit a complex trajectory and are difficult to converge due to the increasing contagion effect. The Empirical results reveal that the transition probabilities of the Chinese traders have only been affected by the contagion effect, so the China's stock market is difficult at this stage to achieve the fundamental price through the market self-regulation.Secondly, by constructing a two-dimensional nonlinear dynamical model of asset prices based on the heterogeneous price expectations,we analyze the evolution and stability of asset prices and discuss the impact of risk free rate adjustment on the fluctuation of asset prices. Furthermore, we use empirical test to study the volatility of China's stock market from 2004 to 2009. It finds that the security market is difficult to form locally stable due to the increasing risk free rate and the stability can not be essentially changed when the risk free rate has declined. In addition, the results are also indirectly confirmed by the empirical work.Thirdly,by allowing investors to trade abroad and have heterogeneous strateges,we present a three-dimensional nonlinear dynamical model with two stock markets and a related foreign exchange market.Separately under closed and open economic circumstance,this paper gains attention to the steady state of asset prices. The findings are as follows.In a closed economy, both the foreign stock market and the foreign exchange market have an unique steady state represented by the fundamental price,and the domestic stock market always admits three steady states.In an open economy,the three makets simultaneously exhibit complex price trajectories and multiple equilibria,however, steady state prices deviating from fundamentals are highly related to the speculative demand of foreign traders in the domestic stock market.To a certain extent,the model can be applied to explain some financial phenomena,such as excess volatility of asset prices.Finally, by integrating Okun's law, a Phillips curve with heterogeneous inflation expectations and an aggregate demand relation, it is presented a three-dimensional nonlinear dynamical model of inflation rate evolution, and gain more attention to dynamics of inflation rate, output growth rate and changes in unemployment rate. This chapter includes four results. Firstly, the stability of inflation rate can be influenced by chartist's extrapolative effect whose critical value is jointly determined by fundamentalist'mean reversion effect and the coefficients of Okun's law and Phillips curve. Secondly, inflation rates would be unpredictable and the hyperinflation might be formed if the extrapolative effect should exceed the critical value. Thirdly, even if the extrapolative effect is still below the critical value, inflation rate's overreaction on the interaction of heterogeneous expectations will lead to the emergence of stagflation in the short run. Finally, a increase in the nominal money growth rate or a decrease in the potential output growth rate may produce the same high level of inflation, but there exist two types of output growth rate and changes in unemployment rate.Due to some new ideas and new perspectives about the complex price evolution of related varibales in economics and finance, this work will enrich the nonlinear pricing theory and macroeconomics.Simutaneously, because of the interaction of heterogeneous agents the results have more necessary micro information for supervisors to make the effective macropolicies.