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Note on the collective theory of risk
Scandinavian Actuarial Journal, 1968Abstract What follows has grown out of a discussion with Carl Philipson following a lecture [1] on the collective theory of risk. Although I give here nothing else but a refined interpretation of Paul Levy's form (see, e.g., [2], p. 322) of identically distributed random variables the result still seems of interest for all those working in the field of
Hans Bühlmann
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Moments of two distributions in collective risk theory
Scandinavian Actuarial Journal, 1977Abstract This paper is motivated by Bartlett (1965) and Beekman (1966) in which approximation methods in collective risk theory are discussed. Here we generalize the results on moments given in these two papers, using less complicated techniques.
Elias Shiu
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Extension of the collective risk theory
Scandinavian Actuarial Journal, 1969Abstract In its original form the collective risk theory is based upon the assumption that the r.v. Y(t), the total amount of claims up to the (operational) time t, is a generalized Poisson process and thus has a d.f. of the form a c.f. of the form where is the generalized c.f. of the claim distribution P(y).
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Stable Lévy motion approximation in collective risk theory
Insurance: Mathematics and Economics, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zbigniew Michna, Aleksander Weron
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Some supplementary researches on the collective risk theory
Scandinavian Actuarial Journal, 1932There are several different systems of risk technic which may be adopted in the mathematical treatment of the collective risk theory. Assuming th.e risk rates practically stabile, the following system, however, seems to be the simplest.
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Some problems in the collective theory of risk
Scandinavian Actuarial Journal, 1950Abstract In most works treating the ruin problem of an insurance company, the probability of ruin some time in the future is chiefly considered. The time variable is thus eliminated, which in most respects simplifies the problem theoretically. But as well from theoretical as from practical points of view it is also of interest to know the probability ...
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When does ruin occur in the collective theory of risk?
Scandinavian Actuarial Journal, 1955Abstract In the discussion on the practical applicability of the collective theory of risk to the insurance field some points have been raised, where it is argued that the conceptions of the theory do not correspond to the conditions prevailing in practice, thus entailing a serious reduction of its working value. Three such points will be considered in
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An extension of the renewal equation and its application in the collective theory of risk
Scandinavian Actuarial Journal, 1970Abstract Let us consider the renewal equation where z(x) and the proper probability distribution F(x) on (0,∞) are given. Let µ = ∫0 ∞ x dF(x), the case µ = ∞ is not excluded. Then the following theorem is equivalent to the renewal theorem (see Feller [2]). Theorem 1.1. If z is directly Riemann integrable and F is not arithmetic, then .
Hans U Gerber
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A note on different models of stochastic processes dealt with in the collective theory of risk
Scandinavian Actuarial Journal, 1956Abstract 1. For the definition of general processes with special regard to those concerned in Collective Risk Theory reference is made to Cramer (Collective Risk Theory, Skandia Jubilee Volume, Stockholm, 1955). Let the independent parameter of such a process be denoted by τ, with the origin at the point of departure of the process and on a scale ...
Carl Philipson
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A review of the collective theory of risk
Scandinavian Actuarial Journal, 1968Carl Philipson
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