weighting link ratios by number of claims

[Kato Mayanja]

In using the chain ladder method. We weight the link ratios by the number of claims from the previous devpt year. Am i correct to think this gives us more reliable development factors, Rj than those obtained by simply taking an arithmetic average of the link ratios ? And that in our statistical model, Cij = Rj * Si + Eij. This will reduce the Eij's since Rj *Si will be tend to be closer to the actual incremental claims, Cij ?

 

[Kato Mayanja]

Am i correct to think the reliability of the chain ladder devpt factors is superior because of the following reasons ?
The more the number of claims then
1. The less volatile the link ratio for that accident year from one devpt year to the following devpt year(thinking law of large numbers!)
2. The more information there is.

 

[John Lee]

Apologies for the delay - but I needed some advice from an ST7 tutor as you've gone beyond CT6.

"Assuming he/she is talking about applying the chain ladder method to a triangle of cumulative claim numbers (rather than claim amounts). In this case, he/she is correct that we weight the link ratios by the cumulative number of claims from the previous development year. (If we were applying it to a triangle of cumulative claim amounts, we would weight the link ratios by the cumulative amounts from the previous development year.)

This just means that we give more weight to those origin years where the volume of claims is higher. Hence, assuming the chain ladder assumptions hold, we would intuitively expect credibility considerations to mean that this is more accurate than just taking a simple average. (I don’t recall seeing people use the simple average much in practice. Also, in practice, there would be other considerations to allow for like the relevance of data from older years, the need to allow for any trends etc)

However, there is a paper called “Unbiased loss development factors” by Daniel M Murphy that argues that the best average to take depends on the assumptions about the error term, and that the simple average is sometimes best (under certain assumptions)"

 

[freesurf]

Selection of link ratios based on the volume-weighted method implicitly assumes that you want to give more credit to years with more data. More data usually means more reliable stats and it has the advantage that it copes better with a growing book. Of course, if you have a material catastrophe in one or a few prior years, you may not want to bias things through vol-all selection. And there may be practical reasons that prevent you from stripping out the large claims (e.g. you are an external consultant and the client can't separate these losses). In such scenarios simple averages may be preferable. Similarly if you think that the growth / shrinking of the book isn't material then simple average may be a better unbiased estimator.