Investment Timing For Individual Real Estate Based On Optimal Stopping Time Approach Under The Stochastic Conditions

The existing literatures of real estate investment under real options' framework have been drawn attention to the modeling of the developers but not very much focused on the individual real estate investment. Furthermore, the modeling of the individual real estate investment only limited to stochastic price of real estate and fixed rent,not considered the rent being stochastic. This paper models the renting-or-buying problem under the stochastic condition of rent ,and solves the problem through stopping time analysis and dynamic programming ,and gives the critical value of optimal stopping decision with a series of conclusions and explicit rule of investment. But the former studies of real estate investment have paid much attention to the optimal decision threshold value ,which were the first passage time and the probability to passage the critical value, and have ignored the passage of threshold value. Considering the passage of threshold value, made some optimal investing timing opportunity seemingly lost the meaning of guild actual investment, the reason for this was that the waiting time was too long or the threshold value couldn't be reached at all. For this,we research the passage of critical value by the first passage time approach(FPT)and to verify the validity of the investment rule in the practical investing decision. Simultaneously we make a comparative static analysis as well as sensibility analysis and numerical analysis for the results . It is significative practically to instruct investment.