The Impact Of Inflation And GDP On Optimal Consumption And Investment Of Investors

With the integration of global financial market and financial derivative product diversification,modern portfolio theory develops constantly and uncertain risk sources in the financial market become more and more,for example,interest rate risk,volatility risk,exchange rate risk and so on.In order to maximize the interests of investors,investors must consider these risks when making investment decisions.However,these risk sources are often described by stochastic differential equations and in order to circumvent uncertain risk,these risks can be hedged through the stochastic control methods.In this paper,we study the optimal consumption and portfolio strategy in the case of inflation risk and gross domestic product(GDP)uncertain risk following a stochastic process.Since the outbreak of the subprime mortgage crisis in 2008,inflation has always been a serious problem and the world's financial markets have undergone great changes and the economic situation has been sluggish.When investors make investment decisions,it is necessary to consider the impact of inflation risk on consumption and investment.On the other hand,GDP is an important manifestation of the overall strength of countries around the world and has certain directive significance to the formulation of national policies.In the long run,the trend of GDP is uncertain,and for a long-term investors,the study of the impact of GDP uncertain risk on optimal consumption and investment is also meaningful.The main content of this paper is the impact of inflation and GDP on optimal consumption and portfolio strategy.The basic framework of this paper is composed of four chapters:The first chapter is the introduction,which mainly explains the research background,research significance,domestic and foreign literature and research framework.In the second chapter,we study the optimal consumption and investment strategy with stochastic volatility under inflation which follows mean reverting process.First of all,the price process of risk assets,inflation process and stochastic volatility process are described,and corresponding stochastic control mathematical model is established;Secondly,in the condition of the investors owning recursive utility,the HJB equation is derived under inflation environment with unit elasticity of intertemporal substitution by using dynamic programming principle,and the approximate solution of the optimal consumption and investment strategy is obtained by using the first-order conditions;Finally,under the conditions of given model parameters,numerical simulation and economic analysis are derived.In the third chapter,we study the influence of GDP parameters on the optimal consumption and portfolio under the growth rate of GDP which follows a stochastic process.First of all,the price processes of risk asset and riskless asset as well as GDP growth rate process are described,furthermore an investor's stochastic control model is established;Secondly,the corresponding HJB equation is derived by using dynamic programming principle,and the closed-form solution of the optimal consumption and investment strategy for power utility function is obtained by using the first-order conditions;Finally,a special case that the GDP growth rate follows a mean reverting process is discussed,and given model parameters,numerical simulation and economic analysis are made.The fourth chapter summarizes the research results of this thesis and puts forward the shortcomings of this thesis and the next research plan.