XploRe Help : INSLundberg

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	insurance
See also:	INSCramer INSDeVylder

Quantlet:		INSLundberg
Description:		produces the Lundberg approximation of ruin probability in infinite time for insurance collective risk model.

Reference(s):

P. Cizek, W. Haerdle, R. Weron (2004): "Statistical Tools for Finance and Insurance"

Usage:	`y = INSLundberg(u, theta, distrib, dparameters)`
Input:
	`u`	scalar, n x 1 vector or m x n matrix, initial capital for risk process
	`theta`	scalar, security loading in insurance collective risk model
	`distrib`	string, name of distribution of claims, either: exponential, gamma, mixofexps, Weibull, lognormal, loggamma, Pareto, Burr or truncPareto.
	`dparameters`	list of scalars, parameters of the following distributions: exponential, gamma, Weibull, lognormal, loggamma, Pareto, Burr or truncPareto list of n x 1 vectors of parameters of "mixofexps" distribution, the first vector are parameters for the exponential distributions and the second one are the weights of mixing.
Output:
	`y`	scalar, n x 1 vector or m x n matrix (same dimension as u), ruin probability given by Lundberg approximation.

Note:

In this example the loss distribution is gamma, safety loading 0.3 and initial capital a vector of values from 0 to 10. The Lundberg approximation exists if the first 3 raw moments of loss distribution exist.

Example:

library("insurance") library("xplore") distrib = "gamma" dparameters = list(0.2,0.7) u = #(0:10) theta = 0.3 y = INSLundberg(u, theta, distrib, dparameters) y

Result:

Contents of y

[ 1,]    0.63333
[ 2,]    0.53674
[ 3,]    0.44196
[ 4,]    0.35635
[ 5,]    0.28276
[ 6,]    0.22156
[ 7,]    0.17185
[ 8,]    0.13217
[ 9,]    0.10094
[10,]    0.076634
[11,]    0.057878

Author: P. Mista, 20031218 license MD*Tech