XploRe Help : INSgDeVylder

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:		INSgDeVylder
Description:		produces the gamma De Vylder 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 = INSgDeVylder(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 gamma De Vylder approximation.

Note:

In this example the loss distribution is chosen to be mixture of 2 exponentials, safety loading 0.3 and initial capital a vector of values from 0 to 10. The gamma De Vylder approximation exists if the first 4 (or at least 3) raw moments of loss distribution exist. For gamma distribution the gamma De Vylder gives the exact result.

Example:

library("insurance") library("distribs") distrib = "mixofexps" dparameters = list( #(0.2,1.5), #(0.3,0.7) ) u = #(0:10) theta = 0.3 y = INSgDeVylder(u, theta, distrib, dparameters) y

Result:

Contents of y

[ 1,]  0.74506
[ 2,]  0.69942
[ 3,]  0.65913
[ 4,]  0.62207
[ 5,]  0.58758
[ 6,]  0.55529
[ 7,]  0.52495
[ 8,]  0.49639
[ 9,]  0.46946
[10,]  0.44405
[11,]  0.42006

Author: P. Mista, 20031218 license MD*Tech