The right time to sell a stock whose price is driven by Markovian noise

Robert C. Dalang, M.-O. Hongler
2004 The Annals of Applied Probability  
We consider the problem of finding the optimal time to sell a stock, subject to a fixed sales cost and an exponential discounting rate \rho. We assume that the price of the stock fluctuates according to the equation dY_t=Y_t(\mu dt+\sigma\xi(t) dt), where (\xi(t)) is an alternating Markov renewal process with values in {\pm1}, with an exponential renewal time. We determine the critical value of \rho under which the value function is finite. We examine the validity of the "principle of smooth
more » ... nciple 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.
doi:10.1214/105051604000000747 fatcat:jhtyrkrzhzedboenmrhh6lbdwu