We consider the problem of finding the optimal time to sell a stock, subject to a fixed sales cost and an exponential discounting rate ρ. We assume that the price of the stock fluctuates according to the equation dYt=Yt(μ dt+σξ(t) dt), where (ξ(t)) is an alternating Markov renewal process with values in {±1}, with an exponential renewal time. We determine the critical value of ρ under which the value function is finite. We examine the validity of the “principle of smooth fit” and use this to give a complete and essentially explicit solution to the problem, which exhibits a surprisingly rich structure. The corresponding result when the stock price evolves according to the Black and Scholes model is obtained as a limit case.
Publié le : 2004-11-14
Classification:
Optimal stopping,
telegrapher’s noise,
piecewise deterministic Markov process,
principle of smooth fit,
60G40,
90A09,
60J27
@article{1099674093,
author = {Dalang, Robert C. and Hongler, M.-O.},
title = {The right time to sell a stock whose price is driven by Markovian noise},
journal = {Ann. Appl. Probab.},
volume = {14},
number = {1},
year = {2004},
pages = { 2176-2201},
language = {en},
url = {http://dml.mathdoc.fr/item/1099674093}
}
Dalang, Robert C.; Hongler, M.-O. The right time to sell a stock whose price is driven by Markovian noise. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp. 2176-2201. http://gdmltest.u-ga.fr/item/1099674093/