XploRe Help : INSSegerdahl

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:	INSdiffin INScordiffin

Quantlet:		INSSegerdahl
Description:		produces the Segerdahl 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 = INSSegerdahl(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 (only if u is a vector or scalar), time horizon for risk process
	`lambda`	scalar, intensity of loss arrivals driven by Poisson 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, 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 Segerdahl approximation.

Note:

In this example the loss distribution is gamma, intesity of loss arrivals 5, safety loading 0.3, initial capital a vector of values from 0 to 10 and time horizon 100. The Segerdahl approximation exists only for light tailed loss distributions.

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 = INSSegerdahl(u, T, lambda, theta, distrib, dparameters) y

Result:

Contents of y

     [ 1,]  0.55717
     [ 2,]  0.43219
     [ 3,]  0.33524
     [ 4,]  0.26004
     [ 5,]  0.20171
     [ 6,]  0.15646
     [ 7,]  0.12136
     [ 8,]  0.094138
     [ 9,]  0.073021
     [10,]  0.056641

Example:

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

Result:

Contents of y

     [ 1,]  0.2517   0.16541  0.11341  0.079176  0.055858
     [ 2,]  0.2915   0.18667  0.12636  0.087517  0.0614
     [ 3,]  0.33088  0.2084   0.13974  0.09618   0.067174
     [ 4,]  0.36863  0.23025  0.15341  0.1051    0.073151
     [ 5,]  0.40366  0.25187  0.16723  0.11423   0.079299
     [ 6,]  0.43515  0.27293  0.18106  0.12347   0.085582
     [ 7,]  0.46256  0.29311  0.19474  0.13277   0.091962
     [ 8,]  0.48567  0.31214  0.20814  0.14205   0.098399
     [ 9,]  0.50453  0.3298   0.22112  0.15123   0.10485
     [10,]  0.51945  0.34594  0.23355  0.16024   0.11128

Author: P. Mista, 20031218 license MD*Tech