The problem of disorder seeks to determine a stopping time which is as close as possible to the unknown time of ’disorder’ when the observed process changes its probability characteristics. We give a partial answer to this question for some special cases of Lévy processes and present a complete solution of the Bayesian and variational problem for a compound Poisson process with exponential jump...

A fast exponential time integration scheme is considered for pricing European and double barrier options in jump-diffusion models. After spatial discretization, the option pricing problem is transformed into the product of a matrix exponential and a vector, while the matrix bears a Toeplitz structure. The shift-and-invert Arnoldi method is then employed for fast approximations to such operation...

An exponential-inverse-exponential {Weibull} regression failure model is introduced. Some of its properties like density function, survival and hazard function are derived. Maximum likelihood estimates the parameters new from censored data obtained. To assess local influence diagnostic(s) on parameter estimates, appropriate matrices Also, global used to detect influential observations. Martinga...

We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds for positive harmonic functions in arbitrary open sets. It applies, e.g., to many subordinate Brownian motions, Lévy processes with and without continuous p...

The stochastic exponential Zt = exp{Mt − M0 − (1/2)〈M,M〉t} of a continuous local martingale M is itself a continuous local martingale. We give a necessary and sufficient condition for the process Z to be a true martingale in the case where Mt = R t 0 b(Yu) dWu and Y is a one-dimensional diffusion driven by a Brownian motion W . Furthermore, we provide a necessary and sufficient condition for Z ...

This paper proposes a statistical test of the martingale hypothesis. It can be used to test whether a given time series is a martingale process against certain non-martingale alternatives. The class of alternative processes against which our test has power is very general and it encompasses many nonlinear non-martingale processes which may not be detected using traditional spectrum-based or var...

We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...