Tag Archives: life

Demography, Pension, Statistics

Your Life in Weeks

1 Comment

This week, I discovered a picture on http://waitbutwhy.com/, which represent a (so-called) typical human life, in weeks,

I found that interesting. But the first problem is that I don’t understand the limit, below: 90 years, that’s not the average life length. That’s not what you should expect to live when you get born. The second problem is that it cannot be as static as it might seem, when you look at the picture. I mean, life expectancy at age 0 is not the same as life expectancy at age 30, or 50. So I did try to make an animated graph, using prospective life tables. Here a code to generate life tables, at different period, for a French population (I distinguish, here male and female)

library(demography)
france.LC1 <- lca(fr.mort,adjust="e0",series="female",years=c(1900,2100))
france.fcast <- forecast(france.LC1,h=100)
L2 <- lifetable(france.fcast)
ex2=L2$ex
L1=lifetable(fr.mort,series="female")
ex1=L1$ex
exF=cbind(ex1,ex2)
france.LC1 <- lca(fr.mort,adjust="e0",series="male",years=c(1900,2100))
france.fcast <- forecast(france.LC1,h=100)
L2 <- lifetable(france.fcast)
ex2=L2$ex
L1=lifetable(fr.mort,series="male")
ex1=L1$ex
exM=cbind(ex1,ex2)
Y=colnames(exF)

Based on those lifetables, we can extract remaining life expectancy, at various ages (say, for instance 50, 51, 52, etc), for someone born on some given year (say 1950). Based on those expected remaining lifetimes, we can plot

picture=function(yearborn=1950,age=50){
k=which(Y==yearborn)
M=diag(exM[,k+0:100])
F=diag(exF[,k+0:100])
par(mfrow=c(1,2))
va=0:(52*100-1)
plot(va%%52,va%/%52,cex=.6,pch=15,col=c("light yellow","light blue","white")[1+
(va>=age*52)*1+(va>(age+M[age+1])*52)*1],ylim=c(100,0),axes=FALSE,xlab="Week",
ylab="Age",main=paste("Man, born on ",yearborn,
", age ",age,sep=""))
axis(1)
axis(2)
plot(va%%52,va%/%52,cex=.6,pch=15,col=c("light yellow","pink","white")[1+
(va>=age*52)*1+(va>(age+F[age+1])*52)*1],ylim=c(100,0),axes=FALSE,xlab="Week",
ylab="Age",main=paste("Woman, born on ",yearborn,
", age ",age,sep=""))
axis(1)
axis(2)}

For instance, if we want the graph above, for someone age 30, born in 1980, we use

picture(1980,30)

Now, if we run a code to get an animated gif, we can get, for someone born in 1950,

and for someone born in 2000

Now, if I could get historical datasets, with the average time spent in schools, ages of retirement, etc, I guess I could add it on the graph. But that’s another story…

Actuarial science, Conferences, GLM, Insurance

Modeling analogies in life and nonlife insurance

Leave a comment

On Wednesday afternoon I will be giving a talk at the SCOR Reserving Seminar. The talk will be on modeling analogies in life and nonlife insurance. We will start by discussing data analogies, based on the Lexis diagram in life insurance and in nonlife (when modeling claims dynamics),

This will induce similarities in datasets used in life models, and in nonlife reserving

Further, in the two cases, logPoisson models are usually used, either to model the number of deaths, or the amount of payment. The main difference is that in nonlife insurance, forecasting future payments is rather simple,

But in life models, unfortunately, we need to forecast the behavior of year based parameters.

Note that this is also the case in nonlife insurance when an inflation factor is introduced.
To go further, the slides are available here.