## ----setup, echo=FALSE, message=FALSE, warning=FALSE--------------------------
library("mbbefd")
#library("knitcitations")
#cleanbib()
#options("citation_format" = "pandoc")
#bib <- read.bibtex("mbbefd.bib")
library(lattice)
my.settings <- canonical.theme(color=FALSE)
my.settings[['fontsize']] = list(text = 8, points = 4)
my.settings[['strip.background']]$col <- "darkgrey"
my.settings[['strip.border']]$col<- "black"
## ----cdfsurv, fig.height=2.5, fig.width=6, echo=FALSE, warning=FALSE, fig.align="center"----
n <- 100
Loss <- seq(1, 150, length=n)
mu <- 4.13
sigma <- 0.29
CDF <- plnorm(Loss, mu, sigma)
Density <- dlnorm(Loss, mu, sigma)
Survival <- 1 - CDF
dat <- data.frame(Loss=rep(Loss, 3),
Value=c(Density, CDF, Survival),
Type=gl(3, n,
labels=c("PDF: f(x)",
"CDF: F(x)",
"SF: S(x)=1-F(x)"),
ordered=TRUE))
xyplot(Value ~ Loss | Type, data=dat, ylab="",
layout=c(3,1), as.table=TRUE, type="l",
par.settings = my.settings,
par.strip.text=list(col="white", font=2),
scales=list(relation="free", alternating=1))
## ----LEV, fig.height=2.5, fig.width=5, echo=FALSE, fig.align="center"---------
alpha <- 100
fxy <- function(x,y,...){
x1 <- as.numeric(x[x<=alpha])
if(panel.number()<2){
panel.polygon(c(x1, rev(x1)),
rev(c(rep(1, length(x1)),
rev(y[x<=alpha]))),
col="skyblue", border=NA)
}else{
panel.polygon(c(x1, rev(x1)),
c(rep(0, length(x1)),
rev(y[x<=alpha])),
col="skyblue", border=NA)
}
panel.xyplot(x,y,...)
#panel.text(x=20, y=0.4, label=paste("LEV[X]", cex=2)
}
xyplot(Value ~ Loss | Type,
data=subset(dat, !Type %in% "PDF: f(x)"),
ylab="",
panel=fxy,
layout=c(2,1), as.table=TRUE, type="l",
par.settings = my.settings,
par.strip.text=list(col="white", font=2),
scales=list(relation="free", alternating=1))
## ----LEV2, fig.height=2.5, fig.width=5, echo=FALSE, fig.align="center"--------
alpha1 <- 80
alpha2 <- 100
xyplot(Value ~ Loss | Type,
data=subset(dat, !Type %in% "PDF: f(x)"),
ylab="",
panel=function(x,y,...){
x1 <- c(x[x >= alpha1 & x<=alpha2])
if(panel.number()<2){
panel.polygon(
c(x1, rev(x1)),
rev(c(rep(1, length(x[x >= alpha1 & x<=alpha2])),
rev(y[x >= alpha1 & x<=alpha2]))),
col="skyblue", border=NA)
}else{
panel.polygon(
c(x1, rev(x1)),
c(rep(0, length(x[x >= alpha1 & x<=alpha2])),
rev(y[x >= alpha1 & x<=alpha2])),
col="skyblue", border=NA)
}
panel.xyplot(x,y,...)
},
layout=c(2,1), as.table=TRUE, t="l",
par.settings = my.settings,
par.strip.text=list(col="white", font=2),
scales=list(relation="free", alternating=1))
## ----checkEL------------------------------------------------------------------
sigma <- sqrt(log(1 + 0.3^2))
mu <- log(65) - sigma^2/2
S <- function(x){ 1 - plnorm(x, mu, sigma) }
(lyr <- integrate(S, 80, 100)$value)
## ----ILF----------------------------------------------------------------------
(ILF <- integrate(S, 0, 100)$value / integrate(S, 0, 80)$value)
## ----ExposureCurve, dev.args=list(pointsize=8), fig.height=3, fig.width=3, fig.align="center"----
MPL <- 200
ExpectedLoss <- 65
Deductible <- seq(0, MPL, 1)
G <- sapply(Deductible, function(x){
LEVx <- integrate(S, 0, x)$value
LEVx/ExpectedLoss
})
plot(Deductible/MPL, G,
t="l", bty="n", lwd=1.5,
main="Exposure Curve",
xlab="Deductible as % of MPL",
ylab="% of expected loss paid by insured",
xlim=c(0,1), ylim=c(0,1))
abline(a=0, b=1, lty=2)
## ----simufit, echo=TRUE, warning=FALSE----------------------------------------
set.seed(123456)
x <- c(rbeta(50, 3, 1/2), rmbbefd(50, 1/2, 1/10))
f1 <- fitDR(x, "mbbefd", method="mle")
summary(f1)
b1 <- bootDR(f1, niter=20)
summary(b1)
## ----denplot, echo=FALSE, fig.height=3.5, fig.width=4, fig.align="center"-----
par(cex.main=0.8, cex.lab=0.8, cex.axis=0.8, cex=0.8)
denscomp(f1, demp=TRUE, main="Histogram and theoretical densities")
## ----bootstrapplot,echo=FALSE, fig.height=5, fig.width=5, fig.align="center"----
par(cex.main=0.8, cex.lab=0.8, cex.axis=0.8, mar=c(2,2,2,2))
plot(b1, enhance=TRUE, main="Bootstrapped value of parameters")
## ----simufit2, echo=TRUE, fig.height=5, fig.width=10, warning=FALSE, fig.align="center"----
f2 <- fitDR(x, "oibeta", method="mle")
f3 <- fitDR(x, "oiunif", method="mle")
gofstat(list(f1, f2, f3))
par(mfrow=c(1, 2))
cdfcomp(list(f1, f2, f3), leg=c("mbbefd", "oibeta", "oiunif"))
denscomp(list(f1, f2, f3), leg=c("mbbefd", "oibeta", "oiunif"),
ylim=c(0,4), xleg="topleft")
## ----simufit3, echo=TRUE, fig.height=3.5, fig.width=3.5, warning=FALSE, fig.align="center"----
par(cex=0.8)
eccomp(list(f1, f2, f3), leg=c("mbbefd", "oibeta", "oiunif"), do.points=FALSE)
## ----SwissReExample, message=FALSE, echo=FALSE, warning=FALSE-----------------
Client <- scan(textConnection(
'150 75 250 200 400 325 600 500 800 700 1000 900 1250 1125 1500 1375 1750 1625 2000 1875 2500 2250 3000 2750 4000 3500 5500 4750 9000 7250 12500 10750 18000 15250 24000 21000 36000 30000 48000 42000 72000 60000 90000 81000'))
MaxMPL <- Client[seq(from=1, to=length(Client),by = 2)]
MeanMPLGrossLoss <- Client[seq(from=2, to=length(Client),by = 2)]
GrossPremium <- scan(textConnection(
'33434 14568 6324 4584 3341 1405 1169 683 613 554 700 552 1194 1490 4177 3527 3249 2712 2588 1988 657 1918'
))
ExposureCurve <- c(rep(1.5,3), rep(2.0,3), rep(3.0, 4), rep(4.0, 12))
ClientData <- data.frame(MaxMPL, MeanMPLGrossLoss,
GrossPremium, ExposureCurve)
ClientData2 <- ClientData
names(ClientData2) <- c("Max MPL '000", "Mean MPL Gross Loss '000",
"Gross Premium '000", "Exposure Curve Parameter c")
library(pander)
panderOptions('big.mark', ',')
panderOptions('table.split.cells', 8)
pander(ClientData2, justify = rep('right', ncol(ClientData2)))
## Example layer
D <- 1.5e3*457/550
L <- 5e3*457/550
MPLoss <- 3.5e6
retainedDed <- D/MPLoss*1000
retainedLoss <- ecMBBEFD(retainedDed, b=swissRe(4)['b'], g=swissRe(4)['g'])
prem <- 1194 * (1 - retainedLoss)
## ----SwissRe2-----------------------------------------------------------------
Premium_rate <- function(Deductible, Limit, MaxMPL,
MeanMPL, GrossPremium, C, ULR){
DedPerMPL <- Deductible / ifelse(MaxMPL < Deductible, Deductible,
ifelse(MaxMPL<Limit, MeanMPL, Limit))
LossShare <- 1 - apply(cbind(DedPerMPL, C), 1,
function(x){
ecMBBEFD(x[1],
b=swissRe(x[2])['b'],
g=swissRe(x[2])['g'])
})
NetPremium <- GrossPremium * ifelse(MaxMPL < Limit, 1,
Limit/MaxMPL)
XL_Premium <- NetPremium * LossShare
# Rate on Line
sum(XL_Premium)/sum(NetPremium)*ULR
}
pr <- Premium_rate(Deductible = D,
Limit = L,
MaxMPL = ClientData$MaxMPL,
MeanMPL = ClientData$MeanMPLGrossLoss,
GrossPremium = ClientData$GrossPremium,
C=ClientData$ExposureCurve, ULR=0.55)