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
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
Total Claim Cost Distribution: Analytical and Numerical Methods / Trudda, Alessandro. - In: PURE MATHEMATICS AND APPLICATIONS. - ISSN 1218-4586. - 18 n.1-2:(2007), pp. 161-176.
Total Claim Cost Distribution: Analytical and Numerical Methods
TRUDDA, Alessandro
2007-01-01
Abstract
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 resultsI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
