Showing papers in "Scandinavian Actuarial Journal in 2001"
TL;DR: In this article, the authors consider dynamic proportional reinsurance strategies and derive the optimal strategies in a diffusion setup and a classical risk model, where optimal is meant in the sense of minimizing the ruin probability.
Abstract: We consider dynamic proportional reinsurance strategies and derive the optimal strategies in a diffusion setup and a classical risk model. Optimal is meant in the sense of minimizing the ruin probability. Two basic examples are discussed.
257 citations
TL;DR: In this article, the authors derived recursive formulas for all the moments of the claim severity and the claims number process of the CRPVR process under regularity conditions, with the same procedure and assuming that all the claimed severity and claims number processes exist.
Abstract: Under regularity conditions, Le´veille´& Garrido [6] gives a derivation of the first two moments (resp. asymptotic) of a Compound Renewal Present Value Risk (CRPVR) process using renewal theory arguments. In this paper, with the same procedure and assuming that all the moments of the claim severity and the claims number process exist, we get recursive formulas for all the moments (resp. asymptotic) of the CRPVR process.
57 citations
TL;DR: In this paper, the authors defined the surplus on a life insurance policy as the difference between the second order retrospective reserve and the first order prospective reserve, and formulated general principles for redistribution of the systematic part of the surplus as bonus.
Abstract: The surplus on a life insurance policy is defined, at any time during the term of the contract, as the difference between the second order retrospective reserve and the first order prospective reserve. General principles for redistribution of the systematic part of the surplus as bonus are formulated, and various special bonus schemes are discussed. Techniques for forecasting future bonuses are worked out in an extended model with stochastic experience basis. Numerical illustrations are provided.
37 citations
TL;DR: In this paper, the authors examined the behavior of extreme value methods in such settings and proposed an adaptation of the popular Hill (1975) estimator, which is argued that the censoring typically cannot exceed 5% for an effective use of the methods suggested.
Abstract: Real claim data sometimes are censored from above at a high value induced by the sum insured. In this note we examine the behaviour of extreme-value methods in such settings and propose an adaptation of the popular Hill (1975) estimator. It is argued that the censoring typically cannot exceed 5% for an effective use of the methods suggested.
37 citations
TL;DR: In this paper, the St. Petersburg Paradox is discussed in terms of doubling strategies, and it is claimed that what was originally thought of as a ''paradox'' can hardly be considered as very surprising today, but viewed in the context of doubling strategy, we get some results that look paradoxical, at least to the practically oriented investor.
Abstract: The classical St. Petersburg Paradox is discussed in terms of doubling strategies. It is claimed that what was originally thought of as a ''paradox'' can hardly be considered as very surprising today, but viewed in terms of doubling strategies, we get some results that look paradoxical, at least to the practically oriented investor.
32 citations
TL;DR: By replacing the exponential growth in a Makeham function with a straight line at very high ages, graduated mortality rates gave an acceptable adherence to observed data as mentioned in this paper, which is the same as the one used in this paper.
Abstract: By replacing the exponential growth in a Makeham function with a straight line at very high ages, graduated mortality rates gives an acceptable adherence to observed data.
24 citations
TL;DR: In this article, a method of continuity analysis of ruin probabilities with respect to variation of parameters governing risk processes is proposed based on the representation of the ruin probability as the stationary probability of a reversed process.
Abstract: A method of continuity analysis of ruin probabilities with respect to variation of parameters governing risk processes is proposed. It is based on the representation of the ruin probability as the stationary probability of a reversed process. We apply Kartashov's technique designed for continuity analysis of stationary distributions of general Markov chains in order to obtain desired continuity estimates. The method is illustrated by the Sparre Andersen and Markov modulated risk models.
19 citations
TL;DR: In this paper, the authors generalized Gerber's and Shiu's results to the case of an arbitrary premium process, where all claims are integer-valued, and showed that this generalization leads to a new formula for the non-ruin probability.
Abstract: In the context of the classical Poisson ruin model Gerber (1988a,b) and Shiu (1987, 1989) have obtained two formulae for the ruin and non ruin probabilities in infinite time. Here these two formulae are generalized to the case of an arbitrary premium process when all claims are integer-valued, as in Picard & Lefevre (1997). Moreover, this generalization throws a new light on the two known formulae and it then leads very simply to a third new formula.
16 citations
TL;DR: In this paper, explicit expressions for the first two moments of fund level and total contributions, when actuarial gains and losses are amortized over N years, and arithmetic rates of return on assets form a moving average process.
Abstract: In the context of the model of pension funding introduced by Dufresne in 1986, explicit expressions are found for the first two moments of fund level and total contributions, when (1) actuarial gains and losses are amortized over N years, and (2) arithmetic rates of return on assets form a moving average process. The results are obtained via a Markovian representation for the bilinear process obtained for the actuarial losses. One conclusion is that the dependence between successive rates of return may have very significant effects on the financial results obtained.
15 citations
TL;DR: In this article, a study of the extent to which aggregate losses due to severe wind storms can be explained by wind measurements was carried out based on 12 years of data for a region, Ska § ne, in southern Sweden.
Abstract: This paper contains a study of the extent to which aggregate losses due to severe wind storms can be explained by wind measurements. The analysis is based on 12 years of data for a region, Ska § ne, in southern Sweden. A previous investigation indicated that wind measurements from six recording stations in Ska § ne was insufficient to obtain accurate prediction. The present study instead uses geostrophic winds calculated from pressure readings, at a regular grid of size 50 kilometres over Ska § ne. However, also this meteorological data set is seen to be insufficient for accurate prediction of insurance risk. The results indicate that currently popular methods of evaluating wind storm risks from meteorological data should not be used uncritically by insurers or reinsurers. Nevertheless, wind data does contain some information on insurance. risks. There is a need for further research on how to use this information to improve risk assessment.
13 citations
TL;DR: In this paper, a five-parameter survival function was proposed to model human mortality in modern female populations, which is not only defined for integers but also suitable for all ages.
Abstract: A single analytical expression for the probability of survival from birth to age x that would hold good for all ages in the entire human life span has been sought for centuries. With an eight-parameter function, Heligman and Pollard achieved this goal, for integer values of x , in 1980. The present paper introduces a five-parameter survival function intended to model human mortality in modern female populations. The introduced function is not only defined for integers. It is defined for all ages.
TL;DR: In this paper, the authors compared four methods for evaluating the convolution of two compound R 1 distributions by counting the number of elementary algebraic operations required, two of which are applicable in general, whereas the remaining two are restricted to the case when the two compound distributions have the same severity distribution.
Abstract: In the present paper we compare four methods for evaluating the convolution of two compound R 1 distributions by counting the numbers of elementary algebraic operations required. Two of the methods are applicable in general, whereas the remaining two are restricted to the case when the two compound distributions have the same severity distribution. This case is discussed separately. We consider in particular the special case when this common severity distribution is concentrated in one, that is, evaluation of the convolution of two R 1 distributions.