XploRe Help : INScordiffin

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:	INSDeVylderfin INSdiffin

Quantlet:		INScordiffin
Description:		produces the corrected diffusion 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 = INScordiffin(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 only 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 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 corrected diffusion 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 1 to 10 and time horizon 100. The corrected diffusion 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 = INScordiffin(u, T, lambda, theta, distrib, dparameters) y

Result:

Contents of y
[ 1,]  0.55671
[ 2,]  0.43168
[ 3,]  0.33471
[ 4,]  0.25951
[ 5,]  0.20118
[ 6,]  0.15595
[ 7,]  0.12088
[ 8,]  0.09368
[ 9,]  0.07260
[10,]  0.05625

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

Result:

Contents of y

[ 1,]  0.23020  0.12563  0.06942  0.03870  0.02173
[ 2,]  0.32386  0.19397  0.11534  0.06827  0.04027
[ 3,]  0.37686  0.23967  0.15055  0.09366  0.05780
[ 4,]  0.41134  0.27214  0.17769  0.11473  0.07336
[ 5,]  0.43572  0.29638  0.19905  0.13218  0.08691
[ 6,]  0.45393  0.31515  0.21622  0.14675  0.09864
[ 7,]  0.46805  0.33011  0.23030  0.15904  0.10881
[ 8,]  0.47933  0.34229  0.24201  0.16950  0.11767
[ 9,]  0.48853  0.35240  0.25189  0.17848  0.12542
[10,]  0.49618  0.36090  0.26032  0.18626  0.13224

Author: P. Mista, 20031218 license MD*Tech