Investment For Individual Real Estate Based On Optimal Stopping Time Approach

Under the real options' framework, most of the existing literatures about the real estateinvestments are mainly concentrated on the modeling of developers, not on the personalreal estate investments. However, as individual investors and consumer issues are trulythe vital interests of millions of ordinary people or medium investors, so pay attentionto the problem of rational investment, so that they will not be troubled by high-riskand uncertainty factors in the housing market, as a result, this is perhaps more deepsociological meaning than concerned the real estate developers. In view of this, the paperwill model such investments.In this thesis, we mainly studs, the following two problems: The first one is that weconstruct a discretization model of stock price in the weak market and establish a modelfor the buying-selling problem. We then investigate the optimal stopping times and thereward of investment. The another one is that we establish a model for the renting-selling problem of personal real estate investment under the price of real estate driven byGeometric Brownian Motion(GBM) and solve this model and give a series of conclusionsand explicit rule of investment, basing the theory of optimal stopping time.Above of all, we recall several results on the optimal stopping time theory, which willplay a basic role in the sequel discussions. Then we consider the price of real estate givenby the following GBM: dp_t=μp_tdt+σp_tdω_t, (1)whereω_t is a one dimension Brownian motions. In order to simulate the nuineriealcalculation, we need to diseretize equation (1) and discuss the diseretizing manner throughthe optimal stopping time theory.Secondly, we pay much attention to the renting-selling problem of personal real estateinvestment, which is ignored in existing literatures, Here we solve this problem basingon the general method and the optimal stopping time theory, and obtain some usefulconclusions.