ABSTRACT
I I Time t
Figure 1.3.1 A sample path of a claim process.
indicat ing the amount of the c la im. T i me is measured to the right
a long the hor izonta l axis and the altitude X of the stepped line at
time t shows the total amount of claims dur ing the time interval
(0, t]. The process is, i n fact, a c o m p o u n d stochastic process i n the
sense that the time of occurrence and the size of each c la im are both
r andom phenomena. A n y part icular realization, consisting of an
observed flow l ike that i n F igure 1.3.1, is called a sample path or a
real izat ion of the process.
