This work examines the problem of sequential detection of a change in the drift of a Brownian motion in the case of two-sided alternatives. Applications to real life situations in which two-sided changes can occur are discussed. Traditionally, 2-CUSUM stopping rules have been used for this problem due to their asymptotically optimal character as the mean time between false alarms tends to $\inf...

Optimization/control problems with change of filtartions have been studied in various context of mathematical finance. This paper studies optimal stopping problems for general diffusion processes with an uncertain time horizon and under different filtrations. Corresponding value functions are first compared and related explicitly to their counterparts without the time uncertainty. To further an...

BACKGROUND The current stopping rule for peginterferon/ribavirin therapy in hepatitis C virus genotype-1 (HCV-1) patients is based on an early virological response (EVR, defined as >2 log(10) viral reduction at treatment week 12). We aimed to explore rapid stopping rules at week 4. METHODS We randomly allocated 528 HCV-1 patients into training and validation sets (at a 1∶2 ratio). The interle...

Let X1 X2 Xn be independent and identically distributed with distribution function F . A statistician may choose two X values from the sequence by means of two stopping rules t1 t2, with the goal of maximizing E Xt1 ∨ Xt2 . We describe the optimal stopping rules and the asymptotic behavior of the optimal expected stopping values, V 2 n , as n → , when F is the exponential distribution. Specific...

Let Xn, . . . , X1 be i.i.d. random variables with distribution function F . A statistician, knowing F , observes the X values sequentially and is given two chances to choose X’s using stopping rules. The statistician’s goal is to stop at a value of X as small as possible. Let V 2 n equal the expectation of the smaller of the two values chosen by the statistician when proceeding optimally. We o...

This note provides a bound of the optimal maximum probability for the multiplicative odds theorem in optimal stopping theory. We deal with an optimal stopping problem which maximizes the probability of stopping on any of the last m successes of a sequence of independent Bernoulli trials of length N, where m and N are predetermined integers satisfying 1 ≤ m < N . This problem is an extension of ...

We propose a new solution method for optimal stopping problems with random discounting for linear diffusions whose state space has a combination of natural, absorbing, or reflecting boundaries. The method uses a concave characterization of excessive functions for linear diffusions killed at a rate determined by a Markov additive functional and reduces the original problem to an undiscounted opt...

Abstract Elementary proofs of classical theorems on pricing perpetual call and put options in the standard Black-Scholes model are given. The method presented does not rely on stochastic calculus and is also applied to give prices and optimal stopping rules for perpetual call options when the stock is driven by a Lévy process with no positive jumps, and for perpetual put options for stocks driv...

Objectives: Component-wise boosting algorithms have evolved into a popular estimation scheme in biomedical regression settings. The iteration number of these algorithms is the most important tuning parameter to optimize their performance. To date, no fully automated strategy for determining the optimal stopping iteration of boosting algorithms has been proposed. Methods: We propose a fully data...

We consider the problem of quickest detection of abrupt changes for processes that are not necessarily independent and identically distributed (i.i.d.) before and after the change. By making a very simple observation that applies to most well-known optimum stopping times developed for this problem (in particular CUSUM and Shiryayev–Roberts stopping rule) we show that their optimality can be eas...