TITLE:
Optimal Stopping Time to Buy an Asset When Growth Rate Is a Two-State Markov Chain
AUTHORS:
Pham Van Khanh
KEYWORDS:
Optimal Stopping Time, Posterior Probability, Threshold
JOURNAL NAME:
American Journal of Operations Research,
Vol.4 No.3,
May
7,
2014
ABSTRACT: In this paper we
consider the problem of determining the optimal time to buy an asset in a position
of an uptrend or downtrend in the financial market and currency market as well
as other markets. Asset price is modeled as a geometric Brownian motion with
drift being a two-state Markov chain. Based on observations of asset prices,
investors want to detect the change points of price trends as accurately as
possible, so that they can make the decision to buy. Using filtering techniques
and stochastic analysis, we will develop the optimal boundary at which
investors implement their decisions when the posterior probability process
reaches a certain threshold.