Abstract
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 sup0≤τ≤T
E[f(M
T
− B
τ], where the supremum is over all stopping times τ adapted to the natural filtration of (B
t
) and f is a nonincreasing convex function. The optimal stopping time τ* is shown to be of ‘bang-bang’ type: τ* ≡ 0 if the drift of the underlying process (B
t
) is negative and τ* ≡ 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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Markov risk mappings and risk-sensitive optimal prediction;Mathematical Methods of Operations Research;2022-11-27
2. Optimal selling time in stock market over a finite time horizon;Acta Mathematicae Applicatae Sinica, English Series;2012-06-10