A Model For Market Closure And Security Investment Portfolio & Consumption Choice

In the study of portfolio optimization problem, one of the most important aspect is how to allocate his money to obtain the best expected utility maximization in the case of considering consumption,when the investor put his money in risk-free bank account (or bonds) and risk stocks.At present, the main way to solve this problem is dynamic programming method and martingale method.The majority of researches have been conducted assume that investors can transact continuously.However,there is a closure periodically for the securities market in re-ality.In the period of closure,there may still exist many uncertain factors,resulting the price of securities is not continuous with the day before when the market open the next day.That is common for us to the price upward.This article studied a model of market closure in the management of securities portfolio and consumption choice. Assume a investor holds two kinds of securities:a bond and a stock. They all face market closure and their price process satisfy the following equations respectively. The investor must determine the optimal proportions of his wealth to allocate to bond and stock both during the market open and close period.We use a very simple and direct method to an important case of utility function-CRRA (Constant Relative Risk Aversion) case to get optimal decision x_t~* and consumption rates(c_t~1)~*, (c_t~2)~* explicitly.This paper is divided into 3 chapters.Chapter 1 introduces the basic concepts to the problem of portfolio and consumption choice,and has an overview of its historical stages of research, research methods, and results from representative.In chapter 2,we divide the securities market into two phases firstly:the open period and the close period first.The give each of the two phases of the mathematical model portfolio investment in stocks and bonds respectively,And gives the definition of admissible.In chapter 3, we present the optimal investment strategy, optimal consumption rate in two stages and the explicit solutions of utility function of wealth of the CRRA case in the model of chapter 2. Then we make a corresponding analysis of the economic significance...