Claim size distributions

2009 ◽  
pp. 69-106
Author(s):  
S. Ramasubramanian
Keyword(s):  
Claim Size ◽  
Size Distributions

scholarly journals Computation of Compound Distributions II: Discretization Errors and Richardson Extrapolation

2000 ◽  
Vol 30 (2) ◽  
pp. 309-331 ◽  
Author(s):  
Rudolf Grübel ◽  
Renate Hermesmeier
Keyword(s):  
Continuous Distribution ◽  
Richardson Extrapolation ◽  
Distribution Functions ◽  
Ruin Probabilities ◽  
Claim Size ◽  
Size Distributions ◽  
Standard Methods ◽  
Discretization Step ◽  
Total Claim ◽  
Panjer Recursion

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.

scholarly journals Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims

Risks ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 104 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Eleni Vatamidou
Keyword(s):  
Laplace Transform ◽  
Error Bounds ◽  
Efficient Algorithm ◽  
Ruin Probability ◽  
Risk Process ◽  
Claim Size ◽  
Size Distributions ◽  
Completely Monotone ◽  
Sparre Andersen Risk Process

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.

scholarly journals On Ordering and Danger of Claim Frequency Distributions

1981 ◽  
Vol 12 (1) ◽  
pp. 72-76 ◽  
Author(s):  
M. J. Goovaerts
Keyword(s):  
Claim Size ◽  
Size Distributions ◽  
Frequency Distributions ◽  
Claim Frequency

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

Simplified bounds on the tails of compound distributions

1997 ◽  
Vol 34 (1) ◽  
pp. 127-133 ◽  
Author(s):  
G. E. Willmot ◽  
Xiaodong Lin
Keyword(s):  
Size Distribution ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Claim Size ◽  
Size Distributions ◽  
Tail Probabilities ◽  
Compound Distributions ◽  
Claim Size Distribution

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.

A simple method to estimate parametric claim size distributions from grouped data

2000 ◽  
Vol 24 (3) ◽  
pp. 495-505 ◽  
Author(s):  
Joachim Brix ◽  
Dietmar Pfeifer
Keyword(s):  
Grouped Data ◽  
Claim Size ◽  
Size Distributions ◽  
Simple Method
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