XploRe Help : INSDeVylderfin

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:	INSexactexpfin INScordiffin

Quantlet:		INSDeVylderfin
Description:		produces the finite De Vylder approximation of ruin probability in finite time horizon for insurance collective risk model.

Reference(s):

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

Usage:	`y = INSDeVylderfin(u, T, lambda, theta, distrib, dparameters)`
Input:
	`u`	scalar, n x 1 vector or m x n matrix, initial capital for risk process
	`T`	scalar or p x 1 vector, time horizon for risk process, vector allowed when u is not a matrix
	`lambda`	scalar, intensity of loss arrivals driven by Poisson 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, p x 1 or n x 1 vector (size of T or u) or p x n matrix or m x n matrix, ruin probability in finite time horizon T given by finite De Vylder approximation.

Note:

In this example the loss distribution is chosen to be gamma, intesity of loss arrivals 5, safety loading 0.3, initial capital a vector of values from 1 to 10 and time horizon 100. The finite De Vylder approximation exists if the first 3 raw moments of loss distribution exist.

Note:

In this example the initial capital is a vector of values from 1 to 5 and time horizon a vector of values from 1 to 10.

Example:

library("insurance") library("xplore") distrib = "gamma" dparameters = list(0.2,0.7) u = #(1:10) T = 100 lambda = 5 theta = 0.3 y = INSDeVylderfin(u, T, lambda, theta, distrib, dparameters) y

Result:

Contents of y

[ 1,]  0.56608
[ 2,]  0.43804
[ 3,]  0.33894
[ 4,]  0.26223
[ 5,]  0.20287
[ 6,]  0.15693
[ 7,]  0.12138
[ 8,]  0.093877
[ 9,]  0.072593
[10,]  0.056127

Example:

library("insurance") distrib = "gamma" dparameters = list(0.2,0.7) u = #(1:5) T = #(1:10) lambda = 5 theta = 0.3 y = INSDeVylderfin(u, T, lambda, theta, distrib, dparameters) y

Result:

Contents of y

[ 1,]  0.24021  0.12582  0.06489  0.03302  0.01661
[ 2,]  0.33569  0.19876  0.11541  0.06587  0.03703
[ 3,]  0.38864  0.24579  0.15255  0.09309  0.05594
[ 4,]  0.42286  0.27873  0.18061  0.11520  0.07242
[ 5,]  0.44697  0.30314  0.20247  0.13330  0.08659
[ 6,]  0.46494  0.32197  0.21993  0.14829  0.09875
[ 7,]  0.47886  0.33693  0.23418  0.16086  0.10924
[ 8,]  0.48997  0.34910  0.24601  0.17151  0.11833
[ 9,]  0.49903  0.35918  0.25596  0.18063  0.12626
[10,]  0.50656  0.36765  0.26444  0.18851  0.13321

Author: P. Mista, 20031218 license MD*Tech