21 citations · 58 across the 11 of their papers we have counts for
11 papers
General tax structures for a Lévy insurance risk process under the Cramér condition
Philip Griffin
We investigate the Levy insurance risk model with tax under Cramér's condition. A direct analogue of Cramér's estimate for the probability of ruin in this model is obtained, togeth…
Cramér's Estimate for the Reflected Process Revisited
R. A. Doney, Philip S. Griffin
The reflected process of a random walk or Lévy process arises in many areas of applied probability, and a question of particular interest is how the tail of the distribution of the…
Sample path behavior of a Lévy insurance risk process approaching ruin, under the Cramér-Lundberg and convolution equivalent conditions
Philip S. Griffin
Recent studies have demonstrated an interesting connection between the asymptotic behavior at ruin of a Lévy insurance risk process under the Cramér-Lundberg and convolution equiva…
Finite Time Ruin Probabilities for Tempered Stable Insurance Risk Processes
Philip S. Griffin, Ross A. Maller, Dale Roberts
We study the probability of ruin before time for the family of tempered stable Lévy insurance risk processes, which includes the spectrally positive inverse Gaussian processes.…
Convolution equivalent Lévy processes and first passage times
Philip S. Griffin
We investigate the behavior of Lévy processes with convolution equivalent Lévy measures, up to the time of first passage over a high level u. Such problems arise naturally in the c…
Small and Large Time Stability of the Time taken for a Lévy Process to Cross Curved Boundaries
Philip S. Griffin, Ross A. Maller
This paper is concerned with the small time behaviour of a Lévy process . In particular, we investigate the {\it stabilities} of the times, $\Tstarb(r)$ and $\Tbarb(r)$, at whic…
The time at which a Lévy process creeps
Philip S. Griffin, Ross A. Maller
We show that if a Lévy process creeps then, as a function of , the renewal function of the bivariate ascending ladder process is absolutely continuous on $…
Stability of the Exit Time for Lévy Processes
Philip S. Griffin, Ross A. Maller
This paper is concerned with the behaviour of a Lévy process when it crosses over a positive level, , starting from 0, both as becomes large and as becomes small. Our ma…
Asymptotic Distributions of the Overshoot and Undershoots for the Lévy Insurance Risk Process in the Cramér and Convolution Equivalent Cases
Philip S Griffin, Ross A Maller, Kees van Schaik
Recent models of the insurance risk process use a Lévy process to generalise the traditional Cramér-Lundberg compound Poisson model. This paper is concerned with the behaviour of t…
Path decomposition of ruinous behavior for a general Lévy insurance risk process
Philip S. Griffin, Ross A. Maller
We analyze the general Lévy insurance risk process for Lévy measures in the convolution equivalence class , , via a new kind of path decomposition. This yie…
Pruitt's Estimates in Banach Space
Philip S. Griffin
Pruitt's estimates on the expectation and the distribution of the time taken by a random walk to exit a ball of radius r are extended to the infinite dimensional setting. It is sho…