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

DOI: 10.4236/ajor.2014.43013   PDF   HTML     4,039 Downloads   5,230 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.


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

[1] Khanh, P. (2012) Optimal Stopping Time for Holding an Asset. American Journal of Operations Research, 2, 527-535.
http://dx.doi.org/10.4236/ajor.2012.24062
[2] Peskir, G. and Shiryaev, A.N. (2006) Optimal Stopping and Free-Boundary Problems (Lectures in Mathematics ETH Lectures in Mathematics. ETH Zürich (Closed). Birkhauser, Basel.
[3] Shiryaev, A.N., Xu, Z. and Zhou, X.Y. (2008) Thou Shalt Buy and Hold. Quantitative Finance, 8, 765-776.
http://dx.doi.org/10.1080/14697680802563732
[4] Guo, X. and Zhang, Q. (2005) Optimal Selling Rules in a Regime Switching Model. IEEE Transactions on Automatic Control, 50, 1450-1455.
[5] Lipster, R.S. and Shiryaev, A.N. (2001) Statistics of Random Process: I. General Theory. Springer-Verlag, Berlin, Heidelberg.
[6] Shiryaev, A.N. (1978, 2008) Optimal Stopping Rules. Springer Verlag, Berlin, Heidelberg.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.