XploRe Help : INSDeVylder

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 INSBeekmanBowers

Quantlet:		INSDeVylder
Description:		produces the 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 = INSDeVylder(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 De Vylder approximation.

Note:

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

Example:

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

Result:

Contents of y
[ 1,]    0.73171
[ 2,]    0.56639
[ 3,]    0.43842
[ 4,]    0.33937
[ 5,]    0.26269
[ 6,]    0.20334
[ 7,]    0.1574
[ 8,]    0.12184
[ 9,]    0.094311
[10,]    0.073003
[11,]    0.056509

Author: P. Mista, 20031218 license MD*Tech