The probability of ruin in finite time with discrete claim size distribution

1997 ◽  
Vol 1997 (1) ◽  
pp. 58-69 ◽  
Author(s):  
Philippe Picard ◽  
Claude Lefèvre
Keyword(s):  
Size Distribution ◽  
Finite Time ◽  
Claim Size ◽  
Probability Of Ruin ◽  
Claim Size Distribution

scholarly journals A class of risk processes with delayed claims: ruin probability estimates under heavy tail conditions

2006 ◽  
Vol 43 (4) ◽  
pp. 916-926 ◽  
Author(s):  
Ayalvadi Ganesh ◽  
Giovanni Luca Torrisi
Keyword(s):  
Size Distribution ◽  
Ruin Probability ◽  
Heavy Tail ◽  
Claim Size ◽  
Probability Estimates ◽  
Claim Size Distribution ◽  
Risk Processes

We consider a class of risk processes with delayed claims, and we provide ruin probability estimates under heavy tail conditions on the claim size distribution.

scholarly journals Excess of Loss Reinsurance with Reinstatements Revisited

2005 ◽  
Vol 35 (01) ◽  
pp. 211-238 ◽  
Author(s):  
Werner Hürlimann
Keyword(s):  
Incomplete Information ◽  
Size Distribution ◽  
Claim Size ◽  
Inverse Gaussian ◽  
Insurance Risk ◽  
Distribution Free ◽  
Analytical Approximations ◽  
Claim Size Distribution ◽  
Aggregate Claims ◽  
Stop Loss

The classical evaluation of pure premiums for excess of loss reinsurance with reinstatements requires the knowldege of the claim size distribution of the insurance risk. In the situation of incomplete information, where only a few characteristics of the aggregate claims to an excess of loss layer can be estimated, the method of stop-loss ordered bounds yields a simple analytical distribution-free approximation to pure premiums of excess of loss reinsurance with reinstatements. It is shown that the obtained approximation is enough accurate for practical purposes and improves the analytical approximations obtained using either a gamma, translated gamma, translated inverse Gaussian or a mixture of the last two distributions.

Tail of compound distributions and excess time

1996 ◽  
Vol 33 (01) ◽  
pp. 184-195 ◽  
Author(s):  
Xiaodong Lin
Keyword(s):  
Size Distribution ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Claim Size ◽  
Compound Distributions ◽  
Fundamental Identity ◽  
Claim Size Distribution ◽  
Simple Bounds ◽  
New Better Than Used ◽  
Better Than

Bounds on the tail of compound distributions are considered. Using a generalization of Wald's fundamental identity, we derive upper and lower bounds for various compound distributions in terms of new worse than used (NWU) and new better than used (NBU) distributions respectively. Simple bounds are obtained when the claim size distribution is NWUC, NBUC, NWU, NBU, IMRL, DMRL, DFR and IFR. Examples on how to use these bounds are given.

scholarly journals A Heuristic Review of some Ruin Theory Results

1985 ◽  
Vol 15 (2) ◽  
pp. 73-88 ◽  
Author(s):  
G. C. Taylor
Keyword(s):  
Size Distribution ◽  
Stochastic Dominance ◽  
Ruin Probability ◽  
Recursion Formula ◽  
Claim Size ◽  
Infinite Time ◽  
Ruin Theory ◽  
Interesting Connection ◽  
Claim Size Distribution ◽  
Aggregate Claims

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.

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.

scholarly journals An Extension of Panjer's Recursion

2002 ◽  
Vol 32 (2) ◽  
pp. 283-297 ◽  
Author(s):  
Klaus Th. Hess ◽  
Anett Liewald ◽  
Klaus D. Schmidt
Keyword(s):  
Size Distribution ◽  
Collective Model ◽  
Risk Theory ◽  
Claim Size ◽  
Similar Characterization ◽  
Claim Number ◽  
Claim Size Distribution ◽  
Aggregate Claims ◽  
Image Position

AbstractSundt and Jewell have shown that a nondegenerate claim number distribution Q = {qn}nϵN0 satisfies the recursionfor all n≥0 if and only if Q is a binomial, Poisson or negativebinomial distribution. This recursion is of interest since it yields a recursion for the aggregate claims distribution in the collective model of risk theory when the claim size distribution is integer-valued as well. A similar characterization of claim number distributions satisfying the above recursion for all n ≥ 1 has been obtained by Willmot. In the present paper we extend these results and the subsequent recursion for the aggregate claims distribution to the case where the recursion holds for all n ≥ k with arbitrary k. Our results are of interest in catastrophe excess-of-loss reinsurance.

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