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 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 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 closed form solution to the perpetual American double barrier call option problem 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 irregular optimal stopping problem to an...

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...

A new algorithm for finding value functions of finite horizon optimal stopping problems in one-dimensional diffusion models is presented. It is based on a time discretization of the corresponding integral equation. The proposed iterative procedure for solving the discretized integral equation...

SFB 649 Discussion Paper 2006-043 An Iteration Procedure for Solving Integral Equations Related to Optimal Stopping Problems Denis Belomestny* Pavel V. Gapeev** * Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany ** Russian Academy of...