Optimal Portfolio Choice With Borrowing Rate Higher Than Deposit Rate When Investing Into A Project

In the study of portfolio optimization problem, an important problem is when investor put his money into a bond (or bank account) and a stock , how to divide his money to get the best result in the case of considering consumption rate. To solve this kind of problem, the dynamic programming method and martingale method are two main method. But in most of papers, they only consider the stock as the risk asset. Few of people consider the usual case where the project can be seen as a risk asset.This paper is mainly about the portfolio choice with borrowing rate higher than deposit rate when the investor invests into a project.This paper is divided into 5 chapters.Chapter 1 is mainly an introduction to the portfolio choice problem with borrowing rate higher than deposit rate when investor invests into a project. An introduction to some existing results is also included.In Chapter 2 , we describe this problem more deeply. It gives us the model of the bond and the project. The expected utility function , value function and wealth equation are also given in this chapter.In Chapter 3, we give the solving procedure using the dynamic programming method. We consider three cases because the relation of ω and π is unknown. Meanwhile we give the optimization result C*(t) and π*(t).In Chapter 4, we consider the special HARA (Hyperbolic Absolute Risk Aversion) case for the three case mentioned in the Chapter 3.Chapter 5 is mainly the analysis of the results of HARA and we also give some economic interpretation for the result in this chapter.