The term moderate deviations is often used in the literature to mean a class of large deviation principles that, some sense, fills gap between convergence probability zero (governed by principle) and weak centered Normal distribution. We talk about non-central when towards non-Gaussian In this paper we study for compound fractional Poisson processes with light-tailed jumps.

Distributions of the first-exit times from a region with non-linear upper boundary are discussed for ordinary and compound Poisson processes. Explicit formulae are developed for the case of ordinary Poisson processes. Recursive formulae are given for the compound Poisson case, where the jumps are positive, having continuous distributions with finite means. Applications to sequential point estim...

We prove the existence of statistical arbitrage opportunities for jump-diffusion models stock prices when jump-size distribution is assumed to have finite moments. show that obtain arbitrage, risky asset holding must go zero in time. Existence demonstrated via ‘buy-and-hold until barrier’ and ‘short strategies with both single double barrier. In order exploit opportunities, investor needs a goo...

Periodicity and Ruin Probabilities for Compound Non-Homogenous Poisson Processes Compound non-homogenous Poisson processes with periodic claim intensity rates are stiidied in this work. A risk process related to a short term periodic environment and the periodicity for its compound claim counting process are discussed. The ruin probabilities of compo~md non-homogenous Poisson processes with per...

In this paper we study first passage times of (reflected) Ornstein–Uhlenbeck processes over compound Poisson-type boundaries. In fact, we extend the results of first rendezvous times of (reflected) Brownian motion and compound Poisson-type processes in Perry, Stadje and Zacks (2004) to the (reflected) Ornstein–Uhlenbeck case.

Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications a...