XploRe Help : INSdiffin

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 INScordiffin

Quantlet:		INSdiffin
Description:		produces the 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 = INSdiffin(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 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 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 diffusion approximation exists if the first 2 raw moments of loss distribution exist.

Note:

In this example the initial capital is a vector of values from 1 to 4 and time horizon a vector of values from 1 to 5.

Example:

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

Result:

Contents of y

     [ 1,]    0.70459
     [ 2,]    0.49642
     [ 3,]    0.34973
     [ 4,]    0.24637
     [ 5,]    0.17354
     [ 6,]    0.12222
     [ 7,]    0.086068
     [ 8,]    0.060599
     [ 9,]    0.042659
     [10,]    0.030023

Example:

library("insurance") library("xplore") distrib = "gamma" dparameters = list(0.2,0.7) u = #(1:4) T = #(1:5) lambda = 5 theta = 0.3 y = INSdiffin(u, T, lambda, theta, distrib, dparameters) y

Result:

Contents of y

[1,]  0.43257  0.13862  0.03178  0.00510
[2,]  0.53489  0.24870  0.09893  0.03327
[3,]  0.58145  0.30939  0.14913  0.06462
[4,]  0.60885  0.34789  0.18518  0.09130
[5,]  0.62710  0.37459  0.21192  0.11303

Author: P. Mista, 20031218 license MD*Tech