Often, sample size is not fixed by design. A key example is a sequential trial with a stopping rule, where stopping is based on what has been observed at an interim look. While such designs are used for time and cost efficiency, and hypothesis testing theory has been well developed, estimation following a sequential trial is a challenging, still controversial problem. Progress has been made in ...

We consider the optimal stopping of independent, discrete time sequences X1, . . . , Xn where m stops are allowed. The payoff is the sum of the stopped values. Under the assumption of convergence of related imbedded point processes to a Poisson process in the plane we derive approximatively optimal stopping times and stopping values. The solutions are obtained via a system of m differential equ...

Many economic situations are modeled as stopping problems. Examples are timing of market entry decisions, search, and irreversible investment. We analyze a principalagent problem where the principal and the agent have di erent preferences over stopping rules. The agent privately observes a signal that in uences his own and the principal's payo . Based on his observation the agent decides when t...

Software stopping rules are tools to effectively minimize the time and cost involved in software testing. The algorithms serve to guide the testing process such that if a certain level of branch or fault (or failure) coverage is obtained without the expectation of further significant coverage, then the testing strategy can be stopped or changed to accommodate further, more advanced testing stra...

Optional stopping refers to the practice of peeking at data and then, based on the results, deciding whether or not to continue an experiment. In the context of ordinary significance-testing analysis, optional stopping is discouraged, because it necessarily leads to increased type I error rates over nominal values. This article addresses whether optional stopping is problematic for Bayesian inf...

A continuous-time version of the multivariate stopping problem is considered. Associated with vector valued jump stochastic processes, stopping problems with a monotone logical rule are defined under the notion of Nash equilibrium point. The existence of an equilibrium strategy and its characterization by integral equations are obtained. Illustrative examples are provided.

The quickest detection problem of a Wiener process for the case of an exponential delay-penalty was recently solved by Beibel. He derived an explicit solution to the problem exploiting the equivalence of this detection problem to an optimal stopping problem of a 2-dimensional degenerate diffusion process. In this publication we shall compute the minimal risk and the optimal stopping rule – with...