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...

The multiple disorder problem consists of finding a sequence of stopping times which are as close as possible to the (unknown) times of 'disorder' when the distribution of an observed process changes its probability characteristics. We present a formulation and solution of the multiple disorder...

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 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 obtain closed-form expressions for the value of the joint Laplace transform of the running maximum and minimum of a diffusion-type process stopped at the first time at which the associated drawdown or drawup process hits a constant level before an independent exponential random time. It is...

Summary A convertible (callable) bond is a security that the holder can convert into a specified number of underlying shares. In addition, the issuer can recall the bond, paying some compensation, or force the holder to convert it immediately. We give an explicit solution to the corresponding...