Autore: Utente:Tomi

Licenza: Gnu FDL

Software usato: R

Panjer

#source('c:/Temp/Panjer.R')
Panjer <- function(k=100,a=0,b=1){
    p0 <- 1;
    p <- c(max(0,a+b)*p0);
    k  <- 2;
    while (p[k-1]>10^(-300)) {
         p <- c(p,p[k-1]*max(0,a+b/k));
         k <- k+1;
         
    }
    p <- c(p0,p)
    p <- p/sum(p);
    return (p);
}

n<-6;
p<-0.45;
k <- seq(0,n)
k0 <- seq(0,n-1)
a <- -p/(1-p)
png('c:/Temp/Panjer-Binomiale.png');
plot(k,
    Panjer(a=a,b=-(n+1)*a)[(k+1)],
    ylim=c(0,0.33),
    xlab=,ylab=,
    type='b',col='red',lwd=2,
    main='v.c. di Panjer - v.c. Binomiale')
lines(k,Panjer(a=a,b=-(n+0.5)*a)[(k+1)],type='b',lwd=2);
lines(k0,Panjer(a=a,b=-(n)*a)[(k0+1)],type='b',col='green',lwd=2);
for (d in c(0.25,.75)) {
   lines(k,Panjer(a=a,b=-(n+d)*a)[(k+1)],type='b')
}
legend(1.8,0.2, 
      c(paste('n =',n),paste('p =',p),'a = -p/(1-p)'),
      bty='n')
legend(1.3,0.12,
      c(paste('b = -(n+',0,')a',sep=),
        paste('b = -(n+',0.25,')a',sep=),
        paste('b = -(n+',0.50,')a',sep=),
        paste('b = -(n+',0.75,')a',sep=),
        paste('b = -(n+',1,')a',sep=),
        ), 
      col = c('green','black','black','black','red'),
      lwd = c(2,1,2,1,2),
      bty='n')
abline(0,0)