In the end of Chapter I we have seen that the optimal stopping problem for a Markov process
X with the value function V is equivalent to the problem of finding the smallest …

The real-time detection of changes in a noisily observed signal is an important problem in
applied science and engineering. The study of parametric optimal detection theory began in …

We introduce a mean field game for a family of filtering problems related to the classic
sequential testing of the drift of a Brownian motion. To the best of our knowledge this work …

We consider the sequential testing of two simple hypotheses for the drift of a Brownian
motion when each observation of the underlying process is associated with a positive cost …

We study the Bayesian problem of sequential testing of two simple hypotheses about the
drift rate of an observable diffusion process. The optimal stopping time is found as the first …

In this paper, we show that the double optimal stopping boundaries for American strangle
options with finite horizon can be characterized as the unique pair of solution to a system of …

Consider the motion of a Brownian particle in three dimensions, whose two spatial
coordinates are standard Brownian motions with zero drift, and the remaining (unknown) …

Consider the motion of a Brownian particle that takes place either in a two-dimensional
plane or in three-dimensional space. Given that only the distance of the particle to the origin …

We study a two-dimensional discounted optimal stopping problem related to the pricing of
perpetual commodity equities in a model of financial markets in which the behaviour of the …

We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of
an arithmetic Brownian motion with the 0-1 loss function and a constant cost of observation …