Let us assume that claims appear in good and bad periods. According to (17.9) we are able to approximate the risk process by:
We can compute finite and infinite time ruin probabilities for
different levels of the initial capital, premium, intensity of claims,
expectation of claims and their variance (see Tables 17.1 and
17.2). We approximate
the finite time ruin probabilities
by formula (17.12) and the infinite time ruin probabilities
using the estimator given in (17.23).
Sample paths of the process are depicted in
Figure 17.1.
The results in the tables show the effects of dependence structures between claims on the crucial
parameter for insurance companies - the ruin probability. Numerical simulations are performed
for different values of the parameter of self-similarity which defines the level of the dependence
between claims. It is clearly visible that an increase of
increases the ruin probability.
The tables also illustrate the relationship between the ruin probability and the initial capital
,
premium
, intensity of claims
, expectation of claims
and their variance
.
It is shown that for dependent damage occurrences the ruin probability is considerably higher than for
independent events.
Thus ignoring possible dependence (existence of good and bad periods) and its level might
lead to wrong choices of the premium
.