The impulse control of a Markov–Feller process is considered when the impulses are allowed only when a signal arrives. This is referred to as an impulse control problem with constraint. A detailed setting is described, a characterization of the optimal cost is obtained using previous results of the authors on optimal stopping problems with constraint, and an optimal impulse control is identified.

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...

A statistical theory for overtraining is proposed. The analysis treats realizable stochastic neural networks, trained with KullbackLeibler loss in the asymptotic case. It is shown that the asymptotic gain in the generalization error is small if we perform early stopping, even if we have access to the optimal stopping time. Considering cross-validation stopping we answer the question: In what ra...

Utility maximization problems of mixed optimal stopping /control type are considered, which can be solved by reduction to a family of related pure optimal stopping problems. Sufficient conditions for the existence of optimal strategies are provided in the context of continuous-time, Itô process models for complete markets. The mathematical tools used are those of optimal stopping theory, contin...

This work compares the performance of all existing 2-CUSUM stopping rules used in the problem of sequential detection of a change in the drift of a Brownian motion in the case of two-sided alternatives. As a performance measure an extended Lorden criterion is used. According to this criterion the optimal stopping rule is an equalizer rule. This paper compares the performance of the modified dri...

Preparing to stop may "prime" the neural mechanism for stopping and alter brain activity at the time of stopping. Much electroencephalography (EEG) research has studied the N2/P3 complex over frontocentral electrodes during outright stopping. Here, we used differential reward of the stop and go processes in a stop signal task to study the sensitivity of these EEG components to preparation. We f...

Equivalences are known between problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping, see for example Karatzas and Shreve [SIAM J. Control Optim. 22 (1984)]. The aim of this paper is to investigate how far connections of this type generalise to a non convex problem of purchasing electricity. Where the classical equivalence break...