Optimal Stock Selling Based on the Global Maximum
20 Pages Posted: 23 Feb 2012
Date Written: February 22, 2012
We aim to determine an optimal stock selling time to minimize the expectation of the square error between the selling price and the global maximum price over a given period. Assuming that stock price follows the geometric Brownian motion, we formulate the problem as an optimal stopping time problem, or equivalently, a variational inequality problem. We provide a partial differential equation (PDE) approach to characterize the resulting free boundary that corresponds to the optimal selling strategy. The monotonicity and smoothness of the free boundary are addressed as well.
Keywords: Optimal selling strategy, global maximum, square error, variational inequality
JEL Classification: Q80 Q35, G60, G40, B91, B28
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