**Optimal Stopping Rules and Their Applications**

The formulation of the general optimal stopping problem: to find a value function V=supτ≤TEGτ, where τ is a stopping time. It is desirable also to find a stopping time τ* such that EGτ*=V (if it exists). Optimal stopping problems are problems of stochastic optimization, and the first works were those of W.A.Shewhart (1920—30, with application to quality control), A.Wald (1940—50, method of sequential analysis).

For many years the author developed the theory of solution of quickest detection problems (change-point problems) whose essence is in determining optimally the time when the observed process changes its characteristics.

In the talk we will expose the general set-up of detection problems and review the solutions of several practical problems based on the methods of stochastic optimization and optimal stopping rules.