Albert N. Shiryaev

On Optimum Methods in Quickest Detection Problems

In this paper optimum methods are developed for observing a process (1), in which the moment when a “disorder”

The cumulant process and Esscher's change of measure

\theta

Local martingales and the fundamental asset pricing theorems in the discrete-time case

appears is not known. The basic quantity characterizing the quality of this observation method is the mean time delay

Quickest Detection Problems in the Technical Analysis of the Financial Data

{\boldsymbol \tau}

Solving the Poisson Disorder Problem

for detection of a disorder.After making assumption (4) it is shown that for a given false alarm probability

Thou shalt buy and hold

\omega

Optimal Stopping Rules and Maximal Inequalities for Bessel Processes

or for a given

On Esscher Transforms in Discrete Finance Models

{\bf N}

A New Look at Pricing of the "Russian Option"

— mathematical expectation of false alarm numbers occurring up to the moment the disorder appears — the observation method minimizing

Stopping Brownian Motion Without Anticipation as Close as Possible to Its Ultimate Maximum

{\boldsymbol \tau } = {\boldsymbol \tau } (\omega)