A Study On Optimal Consumption And Investment With Job Choice And Inflation

The study of the optimal consumption and investment portfolio is one of the most fundamental issues in modern financial theory.The uncertainty of the market environment affects the diversification of portfolios.So how assets can be combined to maximize the interests of investors is one of the basic financial issues that has been studying.Most of the early research on portfolio issues did not take consideration into certain factors,such as labor income,leisure,retirement,work,insurance,interest rate changes etc.However,in the actual situation,these factors have a significant impact on asset allocation.Therefore,in this paper we take the choice of work consider into optimal consumption and investment problems.At the same time,in real life,when investors invest,they also face with a variety of uncertain risks,such as inflation.From a number of studies,we can be found that inflation has a clear impact on investors' optimal consumption and investment strategies.Therefore,we consider the inflation factor into the issue of optimal consumption and investment with job selection.What's more,investors' portfolios generally contain risky assets(such as stocks,funds,futures etc.).This type of asset price change is generally unpredictable and its price is time-dependent.The constant elasticity of variance(CEV)model can well describe the price changes of risk assets.Therefore,in the fourth chapter of this paper,assuming that the risk asset price process satisfies the CEV model,the optimal consumption and investment decision issues with work-selection is studied under inflation.The main content of this paper is to study the impact of inflation on the optimal investment and consumption of investors with job choice.It consists of the following five chapters:The first chapter is composed of three parts.Firstly,the research background and significance of this paper are expounded.Then,the current research status at home and abroad is combed.Finally,the content and structure of the full thesis are summarized.In the second chapter,we examines the effect of inflation on the consumption-investment of investors with work options.Firstly,the investor invests in a risk-free asset(such as bonds)and a risk asset(such as stocks).The agent can choose from two working states,one is high-income and low-leisure and the other is low-income and high-leisure.Then the agent's nominal wealth process can be obtained.What's more,the consumer price index(CPI)is introduced to characterize the inflation process.By using the Ito formula,the process of nominal wealth is discounted into the real wealth process.The agent's preference is characterized by the Cobb-Douglas utility function whose arguments are consumption and leisure.Then,based on maximizing the expected consumption total utility,the closed-form solution of the optimal consumption and investment decision is deduced by using the martingale method.Finally,the effects of inflation factors on optimal consumption and investment strategy are analyzed through numerical simulation.In the third chapter,on the basis of Chapter 2,economic agents'investment are occurred in three types of assets:risk-free assets,inflation index bonds,and risk assets.The role of inflation index bonds is to hedge the risks caused by inflation uncertainty.Based on the thinking of chapter 2,we model and use the martingale and dual method to obtain closed-form solutions for optimal job selection,consumption,and investment decisions.Finally,the analysis of the effects of wealth and inflation volatility on optimal consumption and investment strategies was conducted through numerical simulation.In the forth chapter,on the basis of Chapter 3,We use the CEV model to characterize the price change process of risky assets.Similarly,the CPI is used to characterize the inflation process,and then the investor's real wealth process is obtained after using the Ito formula to discount three assets.Next,the dynamic programming principle is used to obtain the corresponding HJB equations.Finally,based on maximizing the expected consumption total utility,the Legendre transformation method is used and the implicit solution of the agent's optimal consumption and investment are obtained.The last chapter is a summary of the research results of the full thesis,and gives the research inadequacies and aspects that can be improved.