Total Claim Cost Distribution: Analytical and Numerical Methods

The paper examines the problem of determining the distribution
function for random summing of independent, identically distributed (i.i.d.) random
variables. The aim of this paper is to develop a suitable approach to determine
the total claim cost distribution. There are few applications in actuarial
field when the insurance companies look for a given period total damage possible
structure, according to each claim size and policies frequency function. We
try various analytical methods and introduce two numerical approaches which
can be used whenever the solution cannot be derived analytically. Examples
are given to demonstrate that the numerical Laplace anti-transform procedure
is reliable and provides precise approximations of results