scholarly journals On ruin probability and aggregate claim representations for Pareto claim size distributions

2009 ◽  
Vol 45 (3) ◽  
pp. 362-373 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Dominik Kortschak
Keyword(s):  
Ruin Probability ◽  
Claim Size ◽  
Size Distributions ◽  
Aggregate Claim

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 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 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.

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 Approximations of Ruin Probability by Di-Atomic or Di-Exponential Claims

1992 ◽  
Vol 22 (2) ◽  
pp. 235-246 ◽  
Author(s):  
Joshua Babier ◽  
Beda Chan
Keyword(s):  
Ruin Probability ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ruin Probabilities ◽  
Claim Size ◽  
Group Life ◽  
Large Spread ◽  
Claim Size Distribution ◽  
Necessary And Sufficient ◽  
Insurance Data

AbstractThe sensitivity of the ruin probability depending on the claim size distribution has been the topic of several discussion papers in recent ASTIN Bulletins. This discussion was initiated by a question raised by Schmitter at the ASTIN Colloquium 1990 and attempts to make further contributions to this problem. We find the necessary and sufficient conditions for fitting three given moments by diatomic and diexponential distributions. We consider three examples drawn from fire (large spread), individual life (medium spread) and group life (small spread) insurance data, fit them with diatomics and diexponentials whenever the necessary and sufficient conditions are met, and compute the ruin probabilities using well known formulas for discrete and for combination of exponentials claim amounts. We then compare our approximations with the exact values that appeared in the literature. Finally we propose using diatomic and diexponential claim distributions as tools to study the Schmitter problem.

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.

scholarly journals On the expected time to ruin and the expected dividends when dividends are paid while the surplus is above a constant barrier

2005 ◽  
Vol 42 (3) ◽  
pp. 595-607 ◽  
Author(s):  
Esther Frostig
Keyword(s):  
Ruin Probability ◽  
Risk Process ◽  
Claim Size ◽  
Compound Poisson ◽  
Expected Time ◽  
Premium Rate ◽  
Phase Type

We study the expected time to ruin in a risk process in which dividends are paid when the surplus is above the barrier. We consider the case in which the dividend rate is smaller than the premium rate. We obtain results for the classical compound Poisson risk process with phase-type claim size. When the ruin probability is 1, we derive the expected time to ruin and the expected dividends paid. When the ruin probability is less than 1, these quantities are derived conditioning on the event that ruin occurs.

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