XploRe Help : INSPolKhin

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:	INShtraffic INSDeVylder INSrndPK

Quantlet:		INSPolKhin
Description:		produces the simulated ruin probability in infinite time for insurance collecitive risk model, using the Pollaczeck-Khinchine formula.

Reference(s):

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

Usage:	`y = INSPolKhin(u, theta, distrib, dparameters, N, niter)`
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, composed of scalars, (parameters of the following distributions: exponential, gamma, Weibull, lognormal, loggamma, Pareto, Burr or truncPareto) or of n x 1 vectors (parameters of "mixofexps" distribution, the first vector are parameters for the exponential distributions and the second one are the weights of mixing).
	`N`	scalar, number of simulated trajectories from risk process
	`niter`	scalar, number of iterations of the procedure to be repeated
Output:
	`y`	scalar, n x 1 vector or m x n matrix (same dimension as u), ruin probability simulated from Pollaczeck-Khinchine formula.

Note:

In this example the loss distribution is a mixture of 2 exponentials, safety loading 0.3 and initial capital a vector from values 0 to 10. The Pollaczek-Khinchin approximation exists if the first raw moment of loss distribution exists.

Example:

library("insurance") library("distribs") randomize(100) randomize2(100) distrib = "mixofexps" dparameters = list( #(0.2,1.5), #(0.3,0.7) ) u = #(0:10) theta = 0.3 N = 10000 niter = 10 y = INSPolKhin(u, theta, distrib, dparameters, N, niter) y

Result:

Contents of y

 [ 1,]  0.76942
 [ 2,]  0.70234
 [ 3,]  0.65732
 [ 4,]  0.61988
 [ 5,]  0.58675
 [ 6,]  0.55472
 [ 7,]   0.5253
 [ 8,]  0.49747
 [ 9,]  0.47083
 [10,]  0.44609
 [11,]  0.42143

Author: P. Mista, 20041111 license MD*Tech