科研之友
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摘要
Let (B(t))(0 <= t <= T) be either a Bernoulli random walk or a Brownian motion with drift, and let M(t) := max{B(s) : 0 <= s <= t}, 0 <= t <= T. In this paper we solve the general optimal prediction problem sup(0 <=tau <= T) E[f (M(T)-B(tau))], where the supremum is over all stopping times r adapted to the natural filtration of (B(t)) and f is a nonincreasing convex function. The optimal stopping time tau* is shown to be of 'bang-bang' type: tau* equivalent to 0 if the drift of the underlying process (B(t)) is negative and tau* equivalent to T if the drift is positive. This result generalizes recent findings of Toit and Peskir (2009) and Yam, Yung and Zhou (2009), and provides additional mathematical justification for the dictum in finance that one should sell bad stocks immediately, but keep good stocks as long as possible.
- 出版日期2010-12
