卖出价格由马尔可夫噪声驱动的股票的正确时机
The right time to sell a stock whose price is driven by Markovian noise
摘要：
考虑在销售成本固定、折现率为指数函数的情况下，如何确定股票的最佳销售时间。我们假设股票价格按照方程dY_t=Y_t（μdt+σ_t（t）dt）波动，其中（μ dt（t））是一个交替的马尔可夫更新过程，其值在{ \pm 1}中，更新时间为指数。我们确定了ρ的临界值，在此值下，值函数是有限的。我们研究的有效性的“平滑拟合原则”，并使用它来给一个完整的和基本上明确的解决方案的问题，表现出令人惊讶的丰富的结构。作为极限情形，得到了股票价格按Black和Scholes模型演化时的相应结果。
英文摘要：
We consider the problem of finding the optimal time to sell a stock, subject to a fixed sales cost and an exponential discounting rate ρ. We assume that the price of the stock fluctuates according to the equation dY_t=Y_t(μdt+σξ(t) dt), where (ξ(t)) is an alternating Markov renewal process with values in {\pm1}, with an exponential renewal time. We determine the critical value of ρunder 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.
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