Dynamic Analysis Of Macroeconomic System Under Stochastic Conditions

Most of attention of this paper is devoted to intertemporal decision-making model. As stochastic disturbances are added, deterministic decision-making models are extended to stochastic optimal decision models. The continuous time stochastic calculus framework-based stochastic optimization and stochastic dynamic programming, compared with the technique of Markov Chain largely presented in current literatures, are used in the paper to make optimal decision theoretical analysis.In the case of firm investment decision-making, variable q is firstly introduced. By using Ito? formula, random Bellman Equation and Optimal Conditions, an indeterministic q theory model is set up, which can derive optimal time path of control function and explicit solution of the state variables through specific assumption. In the model of quadratic cost function, the optimal control path, not decided by current output and capital stock, depends on the expectations of future output and capital stock. The article also analyzes the inventory investment stochastic model. Followed by the optimal investment decision-making models with specific source of disturbances, we state random perturbation into rates volatility and market demand shocks. By solving models, we obtain the capital's shadow price and the expression of optimal value function, and make correlation analysis of relevant parameters. In the uncertainty demand model, the per capita capital k replaces I as the control variable.In pollution control decision-making model, the disturbances of government spending, production and rates are introduced to derive budget constraint equations. The introduction of pollution into utility function leads to the set-up of a representative individual random intertemporal optimal decision-making model. Adopting the appropriate macroeconomic equilibrium conditions, we calculate best individual environmental investment ratio and the focus on the parameters and benefits analysis. The model firstly involves the individual investment in pollution control, not just by the government to invest in environmental protection ad usual. An important assumption of the model is that individual should pay for the use of environment himself. Another situation is introducing pollution into both utility function and production function with exogenous individual environmental investment ratio. Under certain restrictive conditions, the results from the model are a little different from the first ones. Through discussion of the parameters, the paper firstly uses random analysis of the decision-making model to examine the relations between individual investment of pollution control, government investment in pollution protection and economy growth, social welfare.The paper also discusses a special kind of random decision-making model----Random labor model, of which the core issue is still that the decision-maker pursues maximum of expected discount benefit under random conditions. But the labor market is unique and more uncertain. Some of key variables are discrete. Different from the existing literature in which Markov process is used to describe the state variable, this paper adopts Poisson process to explain the change of state variable. Due to Poisson process's time homogeneous, the value function is not dependent on time, which makes the analysis more concise. We use the Principle of Optimality and the nature of Poisson process to set up a random labor matching model and its extension model, wage-gap model and its dual model. Through the establishment of macroeconomic balance, optimal value and wage distribution are calculated, then we concentrate attention on correlation analysis of variables on the balanced level.Finally, we make some preliminary exploration on the stability of stochastic economic system. Compared with determined type of economic system, current analysis on stability of random-based economy are very small. Solow model is a groundbreaking model in the modern economic growth theory. Based on determined Solow model and introduction of stochastic disturbance into factor accumulation equation, stochastic Solow model is constructed by using Ito? Lemma, which is a stochastic differential dynamic system. The disturbances are described by Brownian Motion. The paper applies quadratic Lyapunov function to discuss stability of the system and concludes that strong disruption to labor would make the system unstable. Random variable's stationary distribution and stationary value are calculated. Then, with the input of human capital, the model becomes a two-dimension form. Further, we introduce technical factor into the model. At this time, the economic system is formed by two departments, that is, material production department and R&D department. The new model is also known as the Lotka-Volterra system. Then,the paper makes system stability analysis on three special circumstances. Currency intervention will change the equation of capital accumulation, thus we build up a stochastic Solow model with currency intervention. While we make stability analysis of the model, per capita capital k is also estimated.