XploRe Help : INSLundbound

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 INSLundberg

Quantlet:		INSLundbound
Description:		produces the Lundberg upper bound for 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 = INSLundbound(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 light-tailed distribution of claims, either: gamma, exponential or mixofexps.
	`dparameters`	list of scalars, parameters of the following distributions: exponential, gamma 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), Lundberg upper bound,

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 upper bound exists only for light tailed loss distributions (adjustment coefficient has to exist).

Example:

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

Result:

Contents of y

[ 1,]          1
[ 2,]    0.77568
[ 3,]    0.60168
[ 4,]    0.46671
[ 5,]    0.36202
[ 6,]    0.28081
[ 7,]    0.21782
[ 8,]    0.16896
[ 9,]    0.13106
[10,]    0.10166
[11,]    0.078854

Author: P. Mista, 20031218 license MD*Tech