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: INSdiffin INScordiffin

 Quantlet: INSSegerdahl Description: produces the Segerdahl 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 = INSSegerdahl(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 (only if u is a vector or scalar), time horizon for risk process 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 Segerdahl 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 0 to 10 and time horizon 100. The Segerdahl 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 = INSSegerdahl(u, T, lambda, theta, distrib, dparameters)
y

```
Result:
```Contents of y

[ 1,]  0.55717
[ 2,]  0.43219
[ 3,]  0.33524
[ 4,]  0.26004
[ 5,]  0.20171
[ 6,]  0.15646
[ 7,]  0.12136
[ 8,]  0.094138
[ 9,]  0.073021
[10,]  0.056641
```
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 = INSSegerdahl(u, T, lambda, theta, distrib, dparameters)
y

```
Result:
```Contents of y

[ 1,]  0.2517   0.16541  0.11341  0.079176  0.055858
[ 2,]  0.2915   0.18667  0.12636  0.087517  0.0614
[ 3,]  0.33088  0.2084   0.13974  0.09618   0.067174
[ 4,]  0.36863  0.23025  0.15341  0.1051    0.073151
[ 5,]  0.40366  0.25187  0.16723  0.11423   0.079299
[ 6,]  0.43515  0.27293  0.18106  0.12347   0.085582
[ 7,]  0.46256  0.29311  0.19474  0.13277   0.091962
[ 8,]  0.48567  0.31214  0.20814  0.14205   0.098399
[ 9,]  0.50453  0.3298   0.22112  0.15123   0.10485
[10,]  0.51945  0.34594  0.23355  0.16024   0.11128
```

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