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

 Quantlet: INShtraffic Description: produces the heavy traffic (diffusion) approximation of ruin probability in infinite time for insurance collective risk model.

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

 Usage: y = INShtraffic(u, theta, distrib, dparameters) 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 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, n x 1 vector or m x n matrix (same dimension as u), ruin probability given by heavy traffic approximation.

Note:
In this example the loss distribution is chosen to be gamma, safety loading 0.3 and initial capital a vector of values from 0 to 10. The heavy traffic approximation exists if the first 2 raw moments of loss distribution exist.

Example:
library("insurance")
library("distribs")
distrib = "gamma"
dparameters = list(0.2,0.7)
u = #(0:10)
theta = 0.3
y = INShtraffic(u, theta, distrib, dparameters)
y

Result:
Contents of y

[ 1,]          1
[ 2,]    0.70469
[ 3,]    0.49659
[ 4,]    0.34994
[ 5,]    0.2466
[ 6,]    0.17377
[ 7,]    0.12246
[ 8,]    0.086294
[ 9,]    0.06081
[10,]    0.042852
[11,]    0.030197

Author: P. Mista, 20031218 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006