Considering The Effects Of Inflation Are The Optimal Investment And Consumption Strategy Research

The problem of optimal investment and consumption refers to the agent’s capital being distributed between consumption and portfolio, expecting maximum utility from terminal wealth and/or intermediate consumption over [0,T] or [0,∞).In this paper, we study the problem of optimal consumption and portfolio considering the impact of inflation when the utility discount function is constant and bounded measurable function, respectively. The paper includes five chapters. In chapter1, firstly, we give a brief introduce on the optimal problem about investment and consumption in continuous-time and the research status in home and abroad, then we put forward the problem that we study in this thesis. In chapter2, we introduce some prepare knowledge about optimal consumption and portfolio in continuous-time. Chapters3and4are the main part of this paper. In Chapter3, supposing the event of individual’s death at event instant of time is an independent Poisson process, we build a stochastic mathematical model with inflation. Applying stochastic analytic, dynamic programming principle and Ito formula, we solve the corresponding optimal control problem, optimal strategies are obtained via Hamilton-Jacobi-Bellman equation. Chapter4, in the complete financial market, we discuss an optimal investment and consumption when the utility discount function is a bounded measurable function on ((0,T],B[0,T]). For the specific constant relative rise aversion utility case, we get the optimal strategies and value function explicitly. The final chapter is the paper’s summery and outlook.