October 2014
Intermediate to advanced
584 pages
22h 2m
English
Content preview from Pricing in General Insurance
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418 Pricing in General Insurance
Hence,
OEPF() [()] Pr
()xxNk
k
k
=− =
=
∞
∑
1
0
(24.3)
In the special case where the frequency distribution is a Poisson, Pr(N = k) = exp(−λ)λ
k
/k!
and after some simple algebra, Equation 24.3 becomes:
OEP(x) = 1 − exp[−λS(x)] (24.4)
where S(x) = 1 − F(x) is the survival probability.
Also, if the frequency distribution is a negative binomial,
Pr
()
()
Nk
kr
k
pp
kr
==
+−
−
1
1
and Equation 24.3 becomes
OEP( )
()
[()]
()
[(
)]
x
p
pF x
p
ppSx
r
r
r
r
=−
−
−
=−
−
−+
1
1
1
1
1
1
(24.5)
An example of how the OEP can be used to calibrate an insurance structure is shown in
Figure 24.5.
24.2.2 Aggregate Exceedance Probability
This is the probability that aggregated ...
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