Results 221 to 230 of about 50,617 (264)
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A note on a classical result in the collective risk theory
Scandinavian Actuarial Journal, 1973Abstract In his paper “Uber einige risikotheoretische Fragestellungen” (SAT 1942: 1–2, p. 43) C.-O. Segerdahl generalizes the theory of ruin probability ψ(u) to the case where interest is continuously added to the risk reserve u at the rate δ′.
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How Close Are the Individual and Collective Models in Risk Theory?
2012The subject of this chapter is individual and collective models in insurance risk theory and how ideal probability metrics can be employed to calculate the distance between them.
Svetlozar T. Rachev +3 more
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An identity in the collective risk theory with some applications
Scandinavian Actuarial Journal, 1968Summary In the present paper we point out and draw some conclusions from the following identity where and Re (z) < 0, and where A(s, z) and B(s, z) are the well-known auxiliary functions used by Cramer in his explicit solution of the ruin problem for a Poisson risk process with risk sums which may assume positive as well as negative values.
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Closed-loop supply chain on the theory of downside-risk based on third-party collecting
2011 Chinese Control and Decision Conference (CCDC), 2011In order to study the impact of risk aversion on the supply chain, a closed loop supply chain model with a risk-neutral manufacturer, a third-party collecting and a downside-risk-averse retailer was established, and the supply chain wasn't coordinated on the theory of downside-risk control.
Cheng-dong Shi, Dun-xin Bian
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On some distributions in time connected with the collective theory of risk
Scandinavian Actuarial Journal, 1970Abstract The title of this paper might as well have been “On the distribution in time of certain first passages in a Poisson process (in the proper sense) with nonzero mean and two barriers, one reflecting or absorbing and the other one absorbing”.
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Some properties of the ruin function in the collective theory of risk
Scandinavian Actuarial Journal, 1948Abstract It is well known that the chief aim of all theory of risk is to attain a sort of objective and somehow confirmed opinion of how and to which extent an insurance company ought to reinsure its risks in order that the probability of ruin by random fluctuations of the risk process shall become so small that it can be overlooked in practice.
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Scandinavian Actuarial Journal, 1948
Abstract 1. The determination of the probability that an insurance company once in the future will be brought to ruin is a problem of great interest in insurance mathematics. If we know this probability, it does not only give us a possibility to estimate the stability of the insurance company, but we may also decide which precautions, in the form of f.
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Abstract 1. The determination of the probability that an insurance company once in the future will be brought to ruin is a problem of great interest in insurance mathematics. If we know this probability, it does not only give us a possibility to estimate the stability of the insurance company, but we may also decide which precautions, in the form of f.
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A semi-convergent series with application to the collective theory of risk
Scandinavian Actuarial Journal, 1952Abstract 1. The Bessel function solution of the differential equation can be numerically calculated by means of the defining power series when x is small. For greater values of x it is more convenient to use an asymptotic expansion. In a paper in this journal, 1950, p.
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A note on transforms of renewal and other models applied to the collective risk theory
Scandinavian Actuarial Journal, 1971Abstract 1. Renewal models applied to the risk theory In this note the interval between the (n—1)th, and the nth event in a random process—the interoccurrence time—will be denoted by τ n for n = 2, 3 ... , and the interval from the starting point of the process to the time point of the first event by τ1.
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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 .
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