The right time to sell a stock whose price is driven by Markovian noise
成果类型：
Article
署名作者：
Dalang, RC; Hongler, MO
署名单位：
Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/105051604000000747
发表日期：
2004
页码：
2176-2201
关键词：
摘要：
We consider the problem of finding the optimal time to sell a stock, subject to a fixed sales cost and an exponential discounting rate P. We assume that the price of the stock fluctuates according to the equation dY(t) = Y-t(mudt + sigmaxi(t)dt), where (xi(t)) is an alternating Markov renewal process with values in {+/-1}, with an exponential renewal time. We determine the critical value of p 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.