### Speaker

### Description

We consider two models of observable process X = (X t ):

Model A: X t = μt + B t ,

Model B: X t = μt + ν(t − θ)^+ + B t ,

where B = (B t ) is a standard Brownian motion, μ and ν are unknown parameters,

and θ is a disorder time.

For Model A, we consider some sequential statistical problems with different

risk functions.

For Model B, we deal with sequential problems of the following type:

H 1 = sup EX τ

or H 2 = sup EE(X τ ),

τ ≤1

τ ≤1

where τ is a stopping time. We show that for such functionals H 1 and H 2 optimal

stopping times have the following form:

τ ∗ = inf{t ≤ 1: ψ(t) ≥ a ∗ (t)},

where ψ(t) is some statistic of observations and a ∗ (t) is a curvilinear boundary

satisfying the Fredholm integral equation of second order. These problems will

be applied to the real asset price models (Apple, Nasdaq).

The talk will gives a survey of the joint papers of authors with Četin,

Novikov, Zhitlukhin, and Muravlev.