| Library: | insurance |
| See also: | INSgam INSwei INSpareto INSlogn |
| Quantlet: | INSbur | |
| Description: | returns pure risk premium for Burr distribution of losses. |
| Usage: | y = INSbur(b,d2,d1,c,m2,m1,lambda,tau,alpha,ind) | |
| Input: | ||
| b | n x 1 vector, deductible (in case of fixed deductible, franchise deductible or proportional deductible) | |
| d2 | n x 1 vector, maximum amount, d2>d1, of linear reduction for disappearing deductible | |
| d1 | scalar, minimum amount of linear reduction for disappearing deductible | |
| c | scalar, deductible (in case of limited proportional deductible) | |
| m2 | n x 1 vector, maximum amount, m2>m1, for limited proportional deductible | |
| m1 | scalar, minimum amount for limited proportional deductible | |
| lambda | scalar, parameter lambda from Burr distribution | |
| tau | scalar, parameter tau from Burr distribution | |
| alpha | scalar, parameter alpha from Burr distribution | |
| ind | scalar, if ind=1, franchise deductible if ind=2, fixed amount deductible if ind=3, proportional deductible if ind=4, limited proportional deductible if ind=5, disappearing deductible | |
| Output: | ||
| y | n x 1 vector, value of the pure risk premium for Burr distribution of losses | |
library("insurance")
library("distribs")
library("plot")
alpha=3.8830 ;alpha parameter in Burr distribution
lambda=1.0891*(10^5) ;lambda parameter in Burr distribution
tau=0.5407 ;tau parameter in Burr distribution
a=(0:100)*100000000 ;argument in payment functions
u1=INSbur(a,0,0,0,0,0,lambda,tau,alpha,1)
u2=INSbur(a,0,0,0,0,0,lambda,tau,alpha,2)
s1 = setmask(a/1000000~u1/1000000,"line","black")
s2=setmask(a/1000000~u2/1000000,"line","red")
plotdisplay = createdisplay(1,1)
show(plotdisplay,1,1,s1,s2)
setgopt(plotdisplay,1,1,"xmajor",5000,"ymajor",200)
setgopt(plotdisplay,1,1,"yvalue",0|1)
setgopt(plotdisplay,1,1,"xvalue",0|1)
setgopt(plotdisplay,1,1,"border",0)
setgopt(plotdisplay,1,1, "xlabel", "Deductible(USD million)", "ylabel", " Premium(USD million)")
setgopt(plotdisplay,1,1,"title","Pure Risk Premium - Burr")
Plot of pure risk premium under franchise deductible (black) and fixed amount deductible (red).
library("insurance")
library("distribs")
library("plot")
alpha=3.8830 ;alpha parameter in Burr distribution
lambda=1.0891*(10^5) ;lambda parameter in Burr distribution
tau=0.5407 ;tau parameter in Burr distribution
m2=(2:100)*1000000000 ;argument in payment functions
c1=0.2 ;parameters c and m1 in the case of limited proportional deductible
c2=0.4
m11=100000000
m12=500000
u1=INSbur(0,0,0,c1,m2,m11,lambda,tau,alpha,4)
u2=INSbur(0,0,0,c2,m2,m11,lambda,tau,alpha,4)
u3=INSbur(0,0,0,c1,m2,m12,lambda,tau,alpha,4)
u4=INSbur(0,0,0,c2,m2,m12,lambda,tau,alpha,4)
s1 = setmask(m2/1000000~u1/1000000,"line","black")
s2=setmask(m2/1000000~u2/1000000,"line","red")
s3 = setmask(m2/1000000~u3/1000000,"line","green")
s4=setmask(m2/1000000~u4/1000000,"line","blue")
plotdisplay = createdisplay(1,1)
show(plotdisplay,1,1,s1,s2,s3,s4)
setgopt(plotdisplay,1,1,"xlim",0|1000)
setgopt(plotdisplay,1,1,"xmajor",200)
setgopt(plotdisplay,1,1,"ymajor",100)
setgopt(plotdisplay,1,1,"yvalue",0|1)
setgopt(plotdisplay,1,1,"xvalue",0|1)
setgopt(plotdisplay,1,1,"border",0)
setgopt(plotdisplay,1,1, "xlabel", "Deductible(USD million)", "ylabel", " Premium(USD million)")
setgopt(plotdisplay,1,1,"title","Pure Risk Premium - Burr")
Plots of pure risk premium under limited proportional deductible with parameters: c1,m11 (black), c2,m11 (red), c1,m12 (green) and c2,m12 (blue).