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

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  • Robert C. Dalang
  • M. -O. Hongler

Abstract

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 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.

Suggested Citation

  • Robert C. Dalang & M. -O. Hongler, 2005. "The right time to sell a stock whose price is driven by Markovian noise," Papers math/0503580, arXiv.org.
    • Handle: RePEc:arx:papers:math/0503580
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