Credibility Theory by Goovaerts, J. and Hoogstad, W.J. and Nationale-Nederlanden

By Goovaerts, J. and Hoogstad, W.J. and Nationale-Nederlanden N.V. Research Dept

Credibility thought prov1des us with techn1ques to figure out insurance
premiums for contracts that belong to a roughly heterogeneous
portfolio, in case there's restricted or abnormal claims exper1ence for
each agreement yet considerable claims adventure for the portfolio. it's the art
and sc1ence of utilizing either types of event to regulate the insurance
premiums and to enhance their accuracy.
The common and by way of now well-known credibility formula
C = (1 - Z) .B + Z.A
originated within the usa in the course of the years sooner than international warfare I and
was recommended within the box of workmen's repayment insurance.
The undefined- huge top class cost charged for a selected occupational class
is represented by means of B. yet an company having a beneficial list w1th this
class attempts to reduce his top rate to A, the speed according to his own
experience. simply because observat1ons of 1 supplier are to a wide extend
ruled through random fluctuations, Whitney [1918) urged a stability C between
the extremes A and B.
Some 70 years in the past he wrote:
"The challenge of expertise ranking arises out of the necess1ty , from
the point of view of fairness to the person probability , of stnk1ng a
balance among class-experience at the one hand and danger exper1ence
on the opposite" .
It used to be felt that the mixing-factor Z may still mirror the amount of the
employer's event. the bigger this quantity, the extra credib1lity, by
means of a excessive price of Z, is hooked up to the specified top rate A. therefore it
became universal parlance to indicate Z as "the credibility issue" or simply
"the credibility". the idea of credibility 1s involved w1th the
quest1on of the way a lot weight can be g1ven to th1s real cla1ms
experience. in fact , not just downward but in addition upward sh1fts 1n
individual charges are attainable, even if the employer's strain 1n such
cases are not felt strongly.

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Extra resources for Credibility Theory

Example text

1. The X. represent average claim amounts. Although we have information on number )S the of claims involved , we deliberately disregard this information . Hence , every contract (or state) attains equal weight. In the next chapters models are introduced that incorporate these weights and supply more reliable credibility estimators for the situation at hand. The results of the model are state j= 1 j= 2 j= 3 j= 4 )2 5 individual estimator M. 95 . 05 . 1671 = 2044. At first sight the value of z is rather high , thus much weight is attached to the ind1vidual experience.

The second assumption reflects the 1ndependence within the contracts and the homogeneity in time. rst the distribution of of hence the classical assumption (B2) can be simplified into E[X. ] J J J = o2 (9 ) . I J t where It denotes the (t x t) identity matr1x and = (Xjl' xj 2 , ... , xjtl . In the next chapters it will xj turn out that the assumptions (Bll and (B2) are rather rigid . In some cases time - homogeneity is felt to be a shortcoming. For instance , in case the X . nated first in order to obtain reliable credibility estimates .

T and are, for all values of p and q, related by for example, a situation where observations on X. amount, pq p JS above a a pq + b pq must correspond on intuitive grounds with outliers. A suitable definition in this case could be d f p min (M , X ) (X ) s p Although in general these functions make this model more flexible than I it is impossible The to incorporate different precisions to the Second, the model is not apt to discover trends like the Hachemeister functions De Vylder p (X ) , ~ s q (9) J non-linear method.

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