Optimal Stopping Time to Buy an Asset When Growth Rate Is a Two-State Markov Chain

Pham Van Khanh

doi:10.4236/ajor.2014.43013

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American Journal of Operations Research > Vol.4 No.3, May 2014

Optimal Stopping Time to Buy an Asset When Growth Rate Is a Two-State Markov Chain ()

Pham Van Khanh

Military Technical Academy, Hanoi, Vietnam.

DOI: 10.4236/ajor.2014.43013 PDF HTML 4,080 Downloads 5,301 Views Citations

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.

Keywords

Optimal Stopping Time, Posterior Probability, Threshold

Share and Cite:

Khanh, P. (2014) Optimal Stopping Time to Buy an Asset When Growth Rate Is a Two-State Markov Chain. American Journal of Operations Research, 4, 132-141. doi: 10.4236/ajor.2014.43013.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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