Risk Management

Read e-book online An introduction to non-life insurance mathematics PDF

By by Bjørn Sundt.

ISBN-10: 3884873989

ISBN-13: 9783884873984

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K). For a risk with level ik of factor k (k=l, ... ,K), the premium is P; ; . It is clear that even with a reasonable number of rating factors 't···•K and levels, the number of possible values of P. could become high, and we 1 1""" 1K could get a voluminous rating book. The rating model should preferably be easy to apply and interpret. Thus we need some sort of structure so that we do not need a separate entry for each combination of rating factors. The simplest solution would presumably be an additive rating model; that is, the premium is determined by Then the insurance agent could add up the parameters for the appropriate levels of the rating factors, and the rating structure could simply consist of the base number tt and the parameter ak,ik for each level ik of each factor k.

8) we see that this property holds more generally for all the transition probabilities Pmn(s,t). 2E. Often it is easier to work with a homogeneous claim number process than with an inhomogeneous one. In this subsection we shall prove a result intro- with ,. n independent oft. duced by Biihlmann (1970) showing how one can in some cases transform an inhomogeneous claim number process into a homogeneous one. Proof. 13). 11) IS I · We easily see that p is continuous, non-decreasing, and satis. an operat"Ion a!

Proof. 13). 11) IS I · We easily see that p is continuous, non-decreasing, and satis. an operat"Ion a! 11). Furthermore, for r2~r1~0 and n~O we have 1 p- ( r) = inf{ t: p( t)=r}. We see that p- Let 1 is non-decreasing, and that which depends on r 1 and r 2 only t hrough. 1 { N( . )} is homogeneous. and p is an operatiOnal time. p be an operational time with corresponding claim intensities "n· r,~o;~~et I -97- -96- ! 12). 2. D. ( t) independent of n. ( t)dt, and this event is independent of the claims history up to time t.

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An introduction to non-life insurance mathematics by by Bjørn Sundt.

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