Showing papers by "Ioannis Karatzas published in 2019"
TL;DR: In this paper, the authors introduce a class of continuous planar processes, called "semimartingales on rays" and develop for them a change-of-variable formula involving quite general classes of test functions.
5 citations
TL;DR: In this paper, the authors considered the problem of optimal stopping in the presence of a quadratic penalty for the estimation error and a fixed, positive cost per unit of observation time.
4 citations
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TL;DR: In this paper, the authors considered the problem of optimal stopping in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit of observation time.
Abstract: Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit of observation time. In a Bayesian framework, where the unobservable drift is assumed to have a known "prior" distribution, this question reduces to choosing judiciously a stopping time for an appropriate diffusion process in natural scale. We establish structural properties of the solution for the corresponding problem of optimal stopping. In particular, we show that, regardless of the prior distribution, the continuation region is monotonically shrinking in time; and provide conditions on the prior distribution guaranteeing a one-sided stopping region. Finally, we illustrate the theoretical results through a detailed study of some concrete prior distributions.