2 You observe the following sample of insurance losses 16 26

2. You observe the following sample of insurance losses: 1.6 2.6 3.1 3.9 4.8 Using a Kernel density model with a uniform kernel with bandwidth 2, estimate the TVaR at the 95 % level for the claim distribution.

Solution

using kernel density model TVAR=K.VAR(X)/nh

so h=bandwidth=2,k=0.95

for variance we have to find mean so mean =1.6+2.6+3.1+3.9+4.8/5=3.2

var=(3.2-1.6)²+(3.2-2.6)²+(3.2-3.1)²+(3.2-3.9)²+(3.2-4.8)²/5

   =5.98/5=1.196

so tvar=0.95*1.196/2=0.5681