Risk Theory

“War is the father of all things”. This sentence of Heraklit (between 540 and 535 BC) has a lot of truth in general. I am quoting it in connection with World War II (1939-1945) and inventions originating in this period. The best known examples of inventions (or first practical use of such invention) are • Nuclear Fission leading to the construction of the atomic bomb and nuclear reactors, • The Programmable Electronic Computer. Best known is the machine of John von Neumann as Los Alamos: Mathematical Analyser Numerical Integrator and Computer (MANIAC), • Radar to guide the airplanes particularly at night and in bad weather conditions, • Penicillin to fight bacteriological diseases. Some of these inventions relied on original discoveries already made before the war, but during the war they were for the first time used on a large scale.

Section: A First Attemptmentioning

confidence: 99%

The History of ASTIN. Invited Lecture at the 50 Years Anniversary of ASTIN

Bühlmann¹

2007

“…Using the Normal Power approximation to the retained risk, with z> 1, one gets (see, for instance, Beard, Pentikainen and Pesonen (1984)…”

Section: The Initial Reserve As a Function Of The Retention Limitmentioning

confidence: 99%

“…AN EXAMPLE Figure 1 shows U{M) when the Normal Power and the Normal approximation are used, for the data used by Beard, Pentikainen and Pesonen (1984), with the exception of the loading coefficient, which is here taking the value 0.25, i.e. for e =0.001…”

Section: ) U(m) = Zo S (M)-(p-e[s]-c(m))mentioning

confidence: 99%

“…For an excess of loss reinsurance arrangement Beard, Pentikainen and Pesonen (1984), p. 146, state the retention problem as the ascertainment of the maximum value of M in such a way that it is granted, with probability 1 -e, that the retained risk will not consume the initial reserve U during the period under consideration. For the effect they have used the Normal Power approximation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Effect of the Retention Limit on the Risk Reserve

Centeno

1995

This paper is devoted to the study of the initial reserve, as a function of the retention limit, needed to assure that the probability of ruin, at the end of a certain period of time, is not higher than an agreed value, for an excess of loss treaty. To assess the probability of ruin, the normal and the normal power approximation are used. It is shown that the initial reserve is not in general an increasing function of the retention, having a minimum under fair assumptions. KEYWORDSRisk reserve; excess of loss; normal power approximation; normal approximation.

“…In particular, the moments are given by simple explicit formulas, confer (3.4), and there exist a number of techniques for computing tail probabilities and fractiles in such distributions, see e.g. BEARD et al (1984).…”

Section: A Review Of Some Properties Of Poisson Distributionsmentioning

confidence: 99%

Prediction of Outstanding Liabilities in Non-Life Insurance

Norberg

1993

142

A fully time-continuous approach is taken to the problem of predicting the total liability of a non-life insurance company. Claims are assumed to be generated by a non-homogeneous marked Poisson process, the marks representing the developments of the individual claims. A first basic result is that the total claim amount follows a generalized Poisson distribution. Fixing the time of consideration, the claims are categorized into settled, reported but not settled, incurred but not reported, and covered but not incurred. It is proved that these four categories of claims can be viewed as arising from independent marked Poisson processes. By use of this decomposition result predictors are constructed for all categories of outstanding claims. The claims process may depend on observable as well as unobservable risk characteristics, which may change in the course of time, possibly in a random manner. Special attention is given to the case where the claim intensity per risk unit is a stationary stochastic process. A theory of continuous linear prediction is instrumental.