Pricing in General Insurance

192 Pricing in General Insurance

14.2.2 Simulating from a Poisson Distribution

Remember the ‘waiting times’ property (Fact 3) in Section 14.2.1: the distribution of wait-

ing times follows an exponential distribution with ‘time constant’ equal to λ: T ~ Exp(λ).

In other terms, the distribution of waiting times has cumulative distribution function (CDF)

F(t) = 1 − exp(−λt) (14.8)

Hence, the waiting time corresponding to a given percentile F(t) is

t

Ft

=−

−( ())ln 1

λ

(14.9)

This suggests a simple algorithm for generating Poisson variates:

# Generating a random number of claims according to the Poisson

distribution

s = 0; n = 0

Do While s < 1

u = rand() ...