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Metainfo.txt
Metainfo.txt
 
 
README.md
README.md
 
 
STFruin13.R
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STFruin13.m
STFruin13.m
 
 
moments.m
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README.md

Visit QuantNet

Visit QuantNet STFruin13 Visit QuantNet 2.0

Name of QuantLet : STFruin13

Published in : Statistical Tools for Finance and Insurance

Description : 'Produces the ruin probability in infinite time for mixture of 2 exponentials
distribution claims given by light traffic approximation. Needs the "moments.m" function.'

Keywords : 'heavy-tailed, pdf, probability, poisson process, approximation, simulation,
exponential, empirical'

See also : 'STFruin02, STFruin03, STFruin04, STFruin05, STFruin06, STFruin07, STFruin08, STFruin09,
STFruin10, STFruin11, STFruin12, STFruin14, STFruin17, moments'

Author : Zografia Anastasiadou

Submitted : Fri, May 04 2012 by Dedy Dwi Prastyo

R Code:

rm(list = ls(all = TRUE))
# setwd('C:/...')

# returns the k-th moment (up to fourth) of the mixture of 2 exponentials distribution claims
moments <- function(k, dparameters) {
    # k: order of moment to calculate dparameters: list, composed of 2 vectors containing the parameters of loss distribution,
    # weights (first vector) and exponential parameters (second vector)
    p1 <- dparameters[[1]]
    p2 <- dparameters[[2]]
    if (k == 1) {
        mk <- sum(p1/p2)
    } else {
        if (k == 2) {
            mk <- 2 * sum(p1/p2^2)
        } else {
            if (k == 3) {
                mk <- 6 * sum(p1/p2^3)
            } else {
                if (k == 4) {
                  mk <- 24 * sum(p1/p2^4)
                }
            }
        }
    }
    return(mk)  # k-th raw moment of the mixture of 2 exponentials distribution claims
}

u <- c(0, 10^9, 5 * 10^9, 10^10, 2 * 10^10, 5 * 10^10)  # initial capital of insurance company (in USD)
theta <- 0.3  # relative safety loading
dparameters1 <- list(c(0.0584, 0.9416), c(3.59e-10, 7.5088e-09))  # weights (first vector) and exponential parameters (second vector)

m <- moments(1, dparameters1)  # 1st raw moment
pa <- matrix(dparameters1[[1]])  # 2 x 1 matrix of weights
pb <- matrix(dparameters1[[2]])  # 2 x 1 matrix of exponential parameters

paa <- matrix(pa, nrow = 2, ncol = length(u))
pbb <- matrix(pb, nrow = 2, ncol = length(u))

d <- rowSums(t(paa/pbb * exp(-pb %*% u)))
c <- matrix(m, nrow = length(d)) - d

# the light traffic approximation for mixture of 2 exponentials claims with \fbeta1=3.5900e-10, beta2=7.5088e-09,
# alpha=0.0584 and theta=0.3 (u in USD)
psi <- (m - c)/(1 + theta)/m

MATLAB Code:

close all
clear all
clc

format long;
u = [0,10.^9,5.*10.^9,10.^10,2.*10.^10,5.*10.^10]';  %initial capital of insurance company (in USD)
theta = 0.3;                                % relative safety loading
dparameters1 = [[0.0584,0.9416]',[3.5900e-10,7.5088e-09]']; % weights (first vector) and exponential parameters (second vector)                               %relative safety loading
m = moments(1,dparameters1);    % 1st raw moment

pa = dparameters1(:,1); % 2 x 1 matrix of weights
pb = dparameters1(:,2); %2 x 1 matrix of exponential parameters

paa = repmat(pa,1,6);
pbb = repmat(pb,1,6);

n = paa./pbb.*exp(-pb*u');
d = sum(n);
c = meshgrid(m,d)-d';
% the light traffic approximation for mixture of 2 exponentials claims with
% beta1=3.5900e-10, beta2=7.5088e-09, alpha=0.0584 and theta=0.3 (u in USD)
psi=(m-c)/(1+theta)/m