scholarly journals A new class of large claim size distributions: Definition, properties, and ruin theory

Bernoulli ◽  
2015 ◽  
Vol 21 (4) ◽  
pp. 2457-2483 ◽  
Author(s):  
Sergej Beck ◽  
Jochen Blath ◽  
Michael Scheutzow
1985 ◽  
Vol 15 (2) ◽  
pp. 73-88 ◽  
Author(s):  
G. C. Taylor

AbstractThe paper deals with the renewal equation governing the infinite-time ruin probability. It is emphasized as intended to be no more than a pleasant ramble through a few scattered results. An interesting connection between ruin probability and a recursion formula for computation of the aggregate claims distribution is noted and discussed. The relation between danger of the claim size distribution and ruin probability is reexamined in the light of some recent results on stochastic dominance. Finally, suggestions are made as to the way in which the formula for ruin probability leads easily to conclusions about the effect on that probability of the long-tailedness of the claim size distribution. Stable distributions, in particular, are examined.


1992 ◽  
Vol 35 (2) ◽  
pp. 64-81
Author(s):  
Robert Knollenberg ◽  
Donald Veal

The sensitivity, resolution, and sample rate of optical particle monitors, counters and spectrometers are described. Important differences in conceptual design of each instrument class are detailed. Optical particle counters and spectrometers require uniform sample volume illumination and have been used in monitoring aerosol microcontamination for many years. Spectrometers have the highest resolution and the greatest number of size channels. Counters may have high intrinsic resolution but it is lost because of the fewer number of size channels provided. Monitors are a relatively new class of instrument which do not provide uniform sample volume illumination. They are becoming widely used in liquid monitoring. Monitors are simpler, less expensive devices and are characterized as having poor resolution but providing the highest sample flow rates and delivering the largest database. When used on fluids with normal populations having an exponential size distribution, monitors show little size distribution distortion. When modal populations or deviations from exponential size distributions are encountered, counters or spectrometers are required. Filter penetration tests generally demand the highest resolution offered only by spectrometers. Data are presented from field visits to 17 semiconductor plants having deionized (D.I.) water processing facilities where monitors and spectrometers were used simultaneously to characterize watcr quality. The data set provides an interesting comparison within the industry as well as an opportunity to compare the low-resolution monitors with high-resolution spectrometers under field conditions.


2000 ◽  
Vol 30 (2) ◽  
pp. 309-331 ◽  
Author(s):  
Rudolf Grübel ◽  
Renate Hermesmeier

AbstractThe standard methods for the calculation of total claim size distributions and ruin probabilities, Panjer recursion and algorithms based on transforms, both apply to lattice-type distributions only and therefore require an initial discretization step if continuous distribution functions are of interest. We discuss the associated discretization error and show that it can often be reduced substantially by an extrapolation technique.


Risks ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 104 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Eleni Vatamidou

We consider the Sparre Andersen risk process with interclaim times that belong to the class of distributions with rational Laplace transform. We construct error bounds for the ruin probability based on the Pollaczek–Khintchine formula, and develop an efficient algorithm to approximate the ruin probability for completely monotone claim size distributions. Our algorithm improves earlier results and can be tailored towards achieving a predetermined accuracy of the approximation.


1981 ◽  
Vol 12 (1) ◽  
pp. 72-76 ◽  
Author(s):  
M. J. Goovaerts

The notion of ordering and danger of claim size distributions is extended to claim frequency distributions.


1997 ◽  
Vol 34 (1) ◽  
pp. 127-133 ◽  
Author(s):  
G. E. Willmot ◽  
Xiaodong Lin

Upper and lower bounds are derived for the tail probabilities of compound distributions using simple properties of the claim size distribution. General bounds are then obtained for various classes of claim size distributions. Some examples are given.


2000 ◽  
Vol 24 (3) ◽  
pp. 495-505 ◽  
Author(s):  
Joachim Brix ◽  
Dietmar Pfeifer

Sign in / Sign up

Export Citation Format

Share Document