Effects of Claims Inflation on ILFs

[Leo Nagi]

Hi,

In the notes when discussing the effects of claims inflation on ILFs the resulting formula is given assuming an inflation of a% affects the loss distribution uniformly been time t and t':

ILFt'(x) = ILFt(x/1+a)/ILFt(b/1+a)

Please could you explain how the above is derived from the basic ILF equation below (including underlying assumptions):

ILFt(x) = LEVx(x)/LEVx(b)

Many thanks,
Leo

 

[Katherine Young]

Hi Leo,

As we say in the Course Notes, the derivation of this formula is beyond the scope of the course. In fact, it's surprisingly hard to find it in the academic literature. Perhaps you can do a deep dive into Google and have better luck than me.

Broadly speaking though the argument is analogous to deflating the limits of a reinsurance layer in order to calculate expected claims cost. Well, think of an event that gives rise to a loss of size b. When inflation is present, we would only require a smaller event, of size b/(1+a), to give rise to that same loss b. We do it this way because it is easier to simply deflate the limit than it is to inflate all the individual claims.

Alternatively, think of an ILF as an index of risk. The higher the risk, the higher the ILF 'index'. Indeed we treat ILFs as though they were an index:

• The index (ie the ILF) starts at 1 for the base layer, and increases in line with the limit for higher layers.
• We calculate the loss cost for a layer with limit i as Ci=Cb*ILF(i). We saw this in equation 3.5 of chapter 15.

Well, when inflation is involved, the expected cost to the layer increases. The risk to the base layer is now based on events of size b/(1+a), since these will now inflate into the layer ... and the risk index (ie the ILF) needs to reflect this. A similar argument applies to ILF(x/1+a).

Best wishes,

Katherine.