
When to Sell an Asset Where Its Drift Drops from a High Value to a Smaller OneDOI: 10.4236/ajor.2015.56040, PP. 514525 Keywords: Optimal Stopping Time, Posterior Probability, Threshold, Markov Chain, Jump Times, Martingale, Brownian Motion Abstract: To solve the selling problem which is resembled to the buying problem in [1], in this paper we solve the problem of determining the optimal time to sell a property in a location the drift of the asset drops from a high value to a smaller one at some random changepoint. This changepoint is not directly observable for the investor, but it is partially observable in the sense that it coincides with one of the jump times of some exogenous Poisson process representing external shocks, and these jump times are assumed to be observable. The asset price is modeled as a geometric Brownian motion with a drift that initially exceeds the discount rate, but with the opposite relation after an unobservable and exponentially distributed time and thus, we model the drift as a twostate Markov chain. Using filtering and martingale techniques, stochastic analysis transform measurement, we reduce the problem to a onedimensional optimal stopping problem. We also establish the optimal boundary at which the investor should liquidate the asset when the price process hit the boundary at first time.
