scholarly journals Estimation of Stop Loss Premium in Fire Insurance

1963 ◽  
Vol 2 (3) ◽  
pp. 356-361 ◽  
Author(s):  
C. P. Welten
Keyword(s):  
Distribution Function ◽  
Fire Insurance ◽  
Stop Loss ◽  
In Fire

The estimation of stop loss premiums can be based on some knowledge about the distribution function of the sum of all claims in a year (assuming that the stop loss insurance relates to a period of one calender year). Generally speaking there are two methods to obtain this knowledge about the distribution function.1. The first method is to construct a distribution function from data concerning:a. the distribution function of the number of claims per year, taking into account the variability of the parameter(s) of this distribution function.b. the distribution function of the insured sums.c. the distribution function of partial claims.d. the correlation between the insured sum and the probability of occurring of a claim.e. the probability of contagion.2. The second method is to derive a distribution function from the year's totals of claims over a long series of years, expressed in e.g: units of the totals of insured sums in that years.In practice it is often difficult to find a useful basis to apply one of these methods. Data concerning the distribution function of the number of claims per year, of the insured sums, and of partial claims are mostly available, but often nothing is known about the correlation between the insured sum and the probability of occurring of a claim.The second method is mostly not applicable because, if the year's totals of claims over a long series of, by preference recent, years are available, these data often turn out to be heterogeneous or to be correlated with time. If, in that case, only the data of the most recent years are used, the number of these data is often a too small basis for the construction of a distribution function.

scholarly journals Modified Recursions for a Class of Compound Distributions

1996 ◽  
Vol 26 (2) ◽  
pp. 213-224 ◽  
Author(s):  
Karl-Heinz Waldmann
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Mass Function ◽  
Cumulative Distribution ◽  
Probability Mass Function ◽  
Initial Value ◽  
Compound Distributions ◽  
Claim Frequency ◽  
Probability Mass ◽  
Stop Loss

AbstractRecursions are derived for a class of compound distributions having a claim frequency distribution of the well known (a,b)-type. The probability mass function on which the recursions are usually based is replaced by the distribution function in order to obtain increasing iterates. A monotone transformation is suggested to avoid an underflow in the initial stages of the iteration. The faster increase of the transformed iterates is diminished by use of a scaling function. Further, an adaptive weighting depending on the initial value and the increase of the iterates is derived. It enables us to manage an arbitrary large portfolio. Some numerical results are displayed demonstrating the efficiency of the different methods. The computation of the stop-loss premiums using these methods are indicated. Finally, related iteration schemes based on the cumulative distribution function are outlined.

scholarly journals Some Remarks on a Recent Paper by Borch

1961 ◽  
Vol 1 (5) ◽  
pp. 265-272 ◽  
Author(s):  
Paul Markham Kahn
Keyword(s):  
Distribution Function ◽  
Random Variable ◽  
Fixed Number ◽  
Point Of View ◽  
Optimum Amount ◽  
Measurable Transformation ◽  
The Difference ◽  
Image Position ◽  
Stop Loss ◽  
Condition B

In his recent paper, “An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance”, presented to the XVIth International Congress of Actuaries, Dr. Karl Borch considers the problem of minimizing the variance of the total claims borne by the ceding insurer. Adopting this variance as a measure of risk, he considers as the most efficient reinsurance scheme that one which serves to minimize this variance. If x represents the amount of total claims with distribution function F (x), he considers a reinsurance scheme as a transformation of F (x). Attacking his problem from a different point of view, we restate and prove it for a set of transformations apparently wider than that which he allows.The process of reinsurance substitutes for the amount of total claims x a transformed value Tx as the liability of the ceding insurer, and hence a reinsurance scheme may be described by the associated transformation T of the random variable x representing the amount of total claims, rather than by a transformation of its distribution as discussed by Borch. Let us define an admissible transformation as a Lebesgue-measurable transformation T such thatwhere c is a fixed number between o and m = E (x). Condition (a) implies that the insurer will never bear an amount greater than the actual total claims. In condition (b), c represents the reinsurance premium, assumed fixed, and is equal to the expected value of the difference between the total amount of claims x and the total retained amount of claims Tx borne by the insurer.

scholarly journals Some Problems Connected with the Calculation of Stop Loss Premiums for Large Portfolios

1967 ◽  
Vol 4 (2) ◽  
pp. 170-174 ◽  
Author(s):  
Fredrik Esscher
Keyword(s):  
Distribution Function ◽  
Expected Number ◽  
Limit Values ◽  
Empirical Determination ◽  
The Mean ◽  
Premium Rates ◽  
Image Position ◽  
Stop Loss ◽  
The Given

When experience is insufficient to permit a direct empirical determination of the premium rates of a Stop Loss Cover, we have to fall back upon mathematical models from the theory of probability—especially the collective theory of risk—and upon such assumptions as may be considered reasonable.The paper deals with some problems connected with such calculations of Stop Loss premiums for a portfolio consisting of non-life insurances. The portfolio was so large that the values of the premium rates and other quantities required could be approximated by their limit values, obtained according to theory when the expected number of claims tends to infinity.The calculations were based on the following assumptions.Let F(x, t) denote the probability that the total amount of claims paid during a given period of time is ≤ x when the expected number of claims during the same period increases from o to t. The net premium II (x, t) for a Stop Loss reinsurance covering the amount by which the total amount of claims paid during this period may exceed x, is defined by the formula and the variance of the amount (z—x) to be paid on account of the Stop Loss Cover, by the formula As to the distribution function F(x, t) it is assumed that wherePn(t) is the probability that n claims have occurred during the given period, when the expected number of claims increases from o to t,V(x) is the distribution function of the claims, giving the conditioned probability that the amount of a claim is ≤ x when it is known that a claim has occurred, andVn*(x) is the nth convolution of the function V(x) with itself.V(x) is supposed to be normalized so that the mean = I.

scholarly journals Expected Value Premium Principle Pada Data Reasuransi

2020 ◽  
Vol 6 (2) ◽  
pp. 21-27
Author(s):  
Radot Mh Siahaan ◽  
Dian Anggraini ◽  
Andi Fitriawati ◽  
Dani Al Makhya
Keyword(s):  
Threshold Value ◽  
Expected Value ◽  
Value Premium ◽  
Fire Insurance ◽  
Pure Premium ◽  
Stop Loss ◽  
Insurance Data

The amount of stop loss cover reinsurance using krone as Danish currency. The stop loss cover reinsurance scheme with a retention value of r = 50 million krone from fire insurance data in Denmark from 1980-1990 with truncate date at 10 million krone, resulting in a conditional expected value that decreases in value when the higher the threshold value. This is indicated by the threshold value of 1 = 2.976 resulting in pure premium of 1 = 0.1217, a threshold value of 2 = 10.0539 resulting in pure premium 2 = 0.0867 and a threshold value of 3 = 26.199 resulting in pure premium 3 = 0.0849. The use of expected value premium principle with the loading factor () is weighted to the value of the pure premium represented by. This is indicated by the weight of premium 1 = 0.13387, the weight of the premium 2 = 0.09537 and the weight of premium 3 = 0.09339.

scholarly journals Risk Measuring Model on Public Liability Fire and Empirical Study in China

2014 ◽  
Vol 9 (1) ◽  
pp. 35-41
Author(s):  
Guo-Xue Gu ◽  
◽  
Shang-Mei Zhao
Keyword(s):  
Risk Factors ◽  
Empirical Study ◽  
Linear Model ◽  
Generalized Linear Model ◽  
Gaussian Kernel ◽  
Favorable Effect ◽  
Public Places ◽  
Fire Insurance ◽  
In Fire

Public fire insurance has recently appeared in China. The basis for calculating the premium is the accurate measurement of Publicliability risk in fire. The generalized linear model (GLM) is widely used for measuring this risk in practice, but the GLM often cannot be satisfied, especially in fat-tailed distribution. A nonparametric Gaussian kernel linear model used to improve the GLM is applied to measure publicliability risk in fire, yielding a favorable effect. Results show three major risk factors that were measured precisely – the nature of the industry, the scale of public places and the level of fire precaution.

scholarly journals The Influence of Climate on Fire Damage

1963 ◽  
Vol 2 (3) ◽  
pp. 345-351 ◽  
Author(s):  
Hans Andersson
Keyword(s):  
Risk Premium ◽  
Geographical Variation ◽  
Building Blocks ◽  
Fire Damage ◽  
Risk Premiums ◽  
Heating Systems ◽  
General Insurance ◽  
Fire Insurance ◽  
The Mean ◽  
In Fire

In his paper “Actuarial Activity in General Insurance in the Northern Countries of Europe” L. Wilhelmsen gives amongst other things an account of the work carried on by Centralstället för nordisk ömsesidig Brandförsäkringsstatistik (CNÖB, the Northern Central Office for Fire Insurance Statistics from Mutual Companies). In this he states that one part of the organisation's work is the carrying out of special investigations of current problems with material collected on each occasion for the purpose.The object of this paper is to report investigations carried out in CNÖB on the connection between temperature and risk premium in fire insurance. The material used is made up exclusively of civil risks (buildings) and the material has been taken from Sweden and Norway. The background to the investigation consists in the fact that in Scandinavia the risk premiums for fire insurance show an apparent geographical variation, in that the amount clearly increases in the most northerly provinces.As we know that the fire damage directly or indirectly caused by heating systems (chimney fires, cracked building blocks, embers from fireplaces or chimneys etc.) represents a large proportion of the damage in civil risks (40-50%, in some materials 60% or more), that the proportion is greatest in the northern parts and that in the Swedish material about 50% of the damage in any one area falls in the four months December to March, it is quite reasonable to trace the influence of the temperature factor behind the geographical variation; the colder the climate, the more lighting of fires and the more damage. This line of argument is connected exclusively to the frequency of damage; we shall return later to the mean degree of damage.

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