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Optimal Stopping Time for Holding an Asset

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Author(s): Pham Van Khanh

Journal: American Journal of Operations Research
ISSN 2160-8830

Volume: 02;
Issue: 04;
Start page: 527;
Date: 2012;
Original page

Keywords: Optimal Stopping Time | Boundary | Brownian Motion | Black-Schole Model

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.
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