Chapter III: Sums and Aggregate Claims

2020 ◽  
pp. 51-83
Author(s):  
Søren Asmussen ◽  
Mogens Steffensen
Keyword(s):  
Aggregate Claims

Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Asymptotic Formula ◽  
Continuous Time ◽  
Heavy Tails ◽  
Tail Behavior ◽  
Renewal Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

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.

On a Dual Model with Multi-Layer Dividend Strategy under Stochastic Interest

2011 ◽  
Vol 422 ◽  
pp. 775-778
Author(s):  
Jin Sheng Yin
Keyword(s):  
Differential Equations ◽  
Poisson Model ◽  
Dual Model ◽  
Exponential Distributions ◽  
Compound Poisson ◽  
Compound Poisson Model ◽  
Surplus Process ◽  
Stochastic Interest ◽  
Aggregate Claims

In insurance mathematics, a compound Poisson model is often used to describe the aggregate claims of the surplus process. In this paper, we consider the dual model of the compound Poisson model with multi-layer dividend strategy under stochastic interest. We derive a set of integro-differential equations satisfied by the expected total discounted dividends until ruin. The cases where profits follow an exponential distributions are solved.

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.

On the distributions of two classes of multiple dependent aggregate claims

2008 ◽  
Vol 24 (4) ◽  
pp. 655-668
Author(s):  
Rong-ming Wang ◽  
Kam C. Yuen ◽  
Li-xing Zhu
Keyword(s):  
Aggregate Claims
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