We consider an optimal stopping problem in a certain model described by a stochastic delay differential equation. We reduce the initial problem to a free-boundary problem of parabolic type and prove the corresponding verification assertion. We also give an example of such an optimal stopping...

We obtain an explicit form of fine large deviation theorems for the log-likelihood ratio in testing models with observed Ornstein-Uhlenbeck processes and get explicit rates of decrease for error probabilities of Neyman-Pearson, Bayes, and minimax tests. We also give expressions for the rates of...

We study a bond market model and related term structure of interest rates where prices of zero coupon bonds are driven by a jump-diffusion process. We present a criterion on the deterministic forward rate volatilities under which the short rate process is Markovian and give sufficient conditions...

We present a solution to some discounted optimal stopping problem for the maximum of a geometric Brownian motion on a finite time interval. The method of proof is based on reducing the initial optimal stopping problem with the continuation region determined by an increasing continuous boundary...

We present a closed form solution to the perpetual American double barrier call option problem in a model driven by Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the inital irregular optimal stopping problem to an...

We present solutions to some discounted optimal stopping problems for the maximum process in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problems to integro-differential free-boundary problems...

We present a solution to the considered in [5] and [22] optimal stopping problem for some jump processes. The method of proof is based on reducing the initial problem to an integro-differential free-boundary problem where the normal reflection and smooth fit may break down and the latter then be...

We present an explicit solution to the formulated in [17] optimal stopping problem for a geometric compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problem to an integro-differential free-boundary problem where the smooth fit may break down...