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: 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
(C) MD*TECH Method and Data Technologies, 05.02.2006