Optimal Stopping Time for Holding an Asset
Author(s)
Pham Van Khanh
ABSTRACT
In this paper, we consider the problem to determine the optimal time to sell an asset that its price conforms to the Black-Schole model but its drift is a discrete random variable taking one of two given values and this probability distribution behavior changes chronologically. The result of finding the optimal strategy to sell the asset is the first time asset price falling into deterministic time-dependent boundary. Moreover, the boundary is represented by an increasing and continuous monotone function satisfying a nonlinear integral equation. We also conduct to find the empirical optimization boundary and simulate the asset price process.
In this paper, we consider the problem to determine the optimal time to sell an asset that its price conforms to the Black-Schole model but its drift is a discrete random variable taking one of two given values and this probability distribution behavior changes chronologically. The result of finding the optimal strategy to sell the asset is the first time asset price falling into deterministic time-dependent boundary. Moreover, the boundary is represented by an increasing and continuous monotone function satisfying a nonlinear integral equation. We also conduct to find the empirical optimization boundary and simulate the asset price process.
Cite this paper
P. Khanh, "Optimal Stopping Time for Holding an Asset," American Journal of Operations Research, Vol. 2 No. 4, 2012, pp. 527-535. doi: 10.4236/ajor.2012.24062.
P. Khanh, "Optimal Stopping Time for Holding an Asset," American Journal of Operations Research, Vol. 2 No. 4, 2012, pp. 527-535. doi: 10.4236/ajor.2012.24062.
References
[1] G. Peskir and A. N. Shiryaev, “Optimal Stopping and Free-Boundary Problems (Lectures in Mathematics ETH Lectures in Mathematics. ETH Zürich (Closed)),” Birkh?user, Basel, 2006. [2] A. N. Shiryaev, Z. Xu and X. Y. Zhou, “Thou Shalt Buy and Hold,” Quantitative Finance, Vol. 8, No. 8, 2008, pp. 765-776. [3] R. S. Lipster and A. N. Shiryaev, “Statistics of Random Process: I. General Theory,” Springer-Verlag, Berlin, Heidelberg, 2001. [4] A. N. Shiryaev, “Optimal Stopping Rules,” Springer- Verlag, Berlin, Heidelberg, 1978, 2008. [5] X. L. Zhang, “Numerical Analysis of American option Pricing in a Jump-Diffusion Model,” Mathematics of Operations Research, Vol. 22, No. 3, 1997, pp. 668-690. doi:10.1287/moor.22.3.668
[1] G. Peskir and A. N. Shiryaev, “Optimal Stopping and Free-Boundary Problems (Lectures in Mathematics ETH Lectures in Mathematics. ETH Zürich (Closed)),” Birkh?user, Basel, 2006. [2] A. N. Shiryaev, Z. Xu and X. Y. Zhou, “Thou Shalt Buy and Hold,” Quantitative Finance, Vol. 8, No. 8, 2008, pp. 765-776. [3] R. S. Lipster and A. N. Shiryaev, “Statistics of Random Process: I. General Theory,” Springer-Verlag, Berlin, Heidelberg, 2001. [4] A. N. Shiryaev, “Optimal Stopping Rules,” Springer- Verlag, Berlin, Heidelberg, 1978, 2008. [5] X. L. Zhang, “Numerical Analysis of American option Pricing in a Jump-Diffusion Model,” Mathematics of Operations Research, Vol. 22, No. 3, 1997, pp. 668-690. doi:10.1287/moor.22.3.668