ABSTRACT
This section begins by studying the properties of the model of section
12.4. It is advisable to begin wi th a simple structure and then proceed
wi th more advanced variants.
(a) Some characteristic properties. Some fundamental features of
the insurance mode l (12.1.1) can be seen from the simplified ratio
form (12.3.6). U s i n g the safety loaded premium, it can be writ ten
u(t) = r(t) • u{t - 1) + p(t) • (1 + l(t)) ~ x(t). (13.1.1)
where now
x(t) = E(x(t)) + EX (13.1.2)
and
p(t) = E(x(t)) + £p. (13.1.3)
These equations w i l l be used in illustrative simulations. In order
to get an approximate idea of the behaviour of the process we assume
that
E(x(t)) = fix = constant. (13.1.4)
Replacing r(t) and k(t) by their mean values r and A, we can eliminate p(t) and x(t) from (13.1.1) and manipulate it into the form
u(t) -u = r-lu(t -l)-S] + su (13.1.5)
where
u = 1 - r
(13.1.6) £u = (l+l)-£p-£x.
