Nash Equilibrium And Sensitivity Analysis On An Investment-Consumption Optimization Problem

Consumption and investment are the most important parts in national income, and is an important goal of fiscal policy. Studying the issue on consumption and investment is of great help for government to develop an effective fiscal policy, make full play of fiscal functions in order to guarantee the rational allocation and rapid growth of income between consumption and investment, and of positive significance in rightly directing fiscal policy and the improving macro-control.The optimization model of consumption and investment establish a link between virtual economy and real economy and contribute a lot to achieving dynamic balance of investment and consumption and provide a new effective way for the realization of the market regulation. Focusing on the impact of market factors and the extent on the consumer’s behavior is not only helpful to improve the behavior of consumer, but also have a significant impact on the improvement of market mechanism and macro-control.Based on the background above and reviewing previous literature on the issue of investment and consumption, the author introduces Nash equilibrium analysis framework——a classical macroeconomics method, to study the optimization of investment and consumption, and uses the maximum likelihood estimation to fit the parameters in the regime switching model, and finally find the optimal strategy of consumption. The author uses data from China and US to carry on the estimation respectively, and the comparison shows China’s capital market is not as stable as US’s market. Then the author numerically analyzes the influence on optimal proportion of consumption by discount rate, time to expiry, market state and the extent of risk aversion. According to the results of the parameter estimation and sensitivity analysis, the author suggests that in order to promote the constant increase of investment and consumption, the government should focus on improving macroeconomic environment, optimize the market structure. Only the market state is sound and stable will the consumer have confidence on the market and increase investment, thus expanding his wealth and ultimately improve the level of consumption.The innovation of this paper is as follows:(1) Special look on this hot issue, this paper focuses on how to avoid the time inconsistency problem, while domestic research mostly focuses on relaxing the assumption of capital market concerned with investment and consumption optimization problem.(2) The author uses data from real market to estimate parameters, which remedies the defect of parameters’estimation in previous study.(3)The author uses the Shanghai Composite Index and S&P500Index daily data as a comparison with a large amount data, which makes the result more persuasive, meanwhile provides theoretic base for promoting China’s capital market.(4)Focusing on the affect on consumption by several market factors make it more precisely on the suggestion.