Review Notes for Loss Models 1 - ACTSC 431/831, FALL 2011
Part 5 – Aggregate Loss Models
Roughly speaking, an aggregate loss model is used to describe the total loss of an insur-
ance portfolio in a ﬁxed time period.
1.
Individual Risk Model:
There are
n
policyholders in an insurance portfolio. Assume
that policyholder
i
will produce a loss/claim of
X
i
, i
= 1
,
2
,...,n.
Then, the total or
aggregate loss of the insurance is
S
n
=
X
1
+
···
+
X
n
.
Such an aggregate loss model is called the individual risk model.
A common example of the individual risk model is that
X
i
=
B
i
I
i
, where
I
i
=
1
,
policyholder
i
makes claims
,
0
,
otherwise
,
and
B
i
>
0 is the total amount of claims by policyholder
i
if it makes claims,
i
= 1
,...,n.
Thus,
S
n
=
B
1
I
1
+
···
+
B
n
I
n
.
2.
Collective Risk Model:
The number of claims in an insurance portfolio is a counting
random variable
N
. The amount of the
i
th claim is
X
i
, i
= 1
,
2
,...
. Then the aggregate
loss/claim of the insurance is
S
=
X
1
+
···
+
X
N
with
S
= 0 if
N
= 0. Such an aggregate loss model is called the collective risk model.
Note that unless stated otherwise, in a collective risk model, we assume that
N,X
1
,X
2
,...
are independent and