A Study On Optimal Consumption-Investment And Retirement Choice Problem Under Inflation

The problem of optimal consumption and investment is a hot topic in the study of economics and finance.The theory was originated from the research of Merton.The behavior of individual investment decisions is the core of the research on consumption and portfolio selection theory.Everyone has to make the decisions for the consumption and portfolio.Therefore,it is of great significance to study the problem of optimal consumption and investment portfolio.However,with the changes of era,in order to maximize the returns of investors,they need to make a portfolio because of the uncertainty of the market environment.Based on the research of Merton,we consider some factors in real life,such as subsistence consumption constraints,leisure,retirement,income and so on.All these factors have a significant impact on asset allocation.In this thesis we consider the problem of optimal consumption and investment with retirement.Due to the development of economy globalization,affected by the financial crisis,the economy of the world,including China,has been affected by inflation.Inflation will affect the judgment of the agents' portfolio.It's imperative for agents considering the impact oninvestment and consumption in inflation under the pressure.Therefore,this thesis studies the problem of optimal investment、consumption and voluntary retirement with a CRRA utility function for agents under inflation and inflation obey mean reverting process.The full thesis is composed of five chapters:The first chapter is introduction,which contains three parts.First of all,the background and significance of this thesis are expounded;then,current domestic and foreign research status are discussed;finally,the contents and structure of this thesis are summarized.In the second chapter,we investigate an optimal consumption/portfolio with voluntary retirement and subsistence consumption constraints under inflation.Firstly,to assume that the investor invests in a risk-free asset(such as bonds)and a risk asset(such as stocks).What's more,the consumer price index(CPI)is introduced to characterize the inflation process.By using Ito formula,the process of nominal wealth is discounted into the real wealth process.To assume that the agent's utility function of consumption is of CRRA type.Then,based on maximizing the expected discounted utility of consumption both before and after retirement,the corresponding HJB equation is established by applying the dynamic programming method.Furthermore,the strategies for the optimal consumption/portfolio and retirement are derived.Finally,we analyses the conclusion through using a numerical simulation.Meanwhile,the economic explanations are given.In the third chapter,on the basis of Chapter 2,agents invest 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,the strategies for the optimal consumption/portfolio and retirement time are derived by applying the dynamic programming method.Finally,the economic explanations are given.In the forth chapter,we establish a model under inflation obey mean reverting process.By using Ito formula,the process of nominal wealth is discounted into the real wealth process.Based on maximizing the expected discounted utility of consumption both before and after retirement,by applying the dynamic programming method and the Legendre transformation method,the strategies for the optimal consumption and portfolio are derived.The last chapter is a summary of the research results.The inadequacies of research and the future research plan are discussed as well.