dfCorTest: Testing for Correlations between Subsequent Development... In ChainLadder: Statistical Methods and Models for Claims Reserving in General Insurance

Description

One of the main assumptions underlying the chain ladder method is the uncorrelation of subsequest development factor. The function tests this assumption.

Usage

 1 dfCorTest(Triangle, ci = .5)

Arguments

 Triangle cumulative claims triangle. Assume columns are the development period, use transpose otherwise. A (mxn)-matrix C_{ik} which is filled for k ≤q n+1-i; i=1,…,m; m≥q n , see qpaid for how to use (mxn)-development triangles with m

Details

As described by the Mack's 1994 paper a procedure is designed to test for calendar year influences.

The usual test for uncorrelatedness requires that we have identically distributed pairs of observations which come from a Normal distribution. Both conditions are usually not fulfilled for adjacent columns of development factors. Spearman's correlation coefficient is therefore used.

The metric calulated by the procudeure described return a statistic T that it is assumed to be Normally Distributed. It is therefore possible to define a confidence interval threshold in order to evaluate the outcome of the test.

Value

dfCorTest returns a list with the following elements

 T_stat summary statistic Var variance of the resulting distribution Range vector of the range corresponding the confidence interval threshold selected ci confidence interval

Note

Thomas Mack. Distribution-free calculation of the standard error of chain ladder reserve estimates. Astin Bulletin. Vol. 23. No 2. 1993. pp.213:225

Thomas Mack. The standard error of chain ladder reserve estimates: Recursive calculation and inclusion of a tail factor. Astin Bulletin. Vol. 29. No 2. 1999. pp.361:366

Venter, G.G., Testing the Assumptions of Age-to-Age Factors, Proceedings of the Casualty Actuarial Society LXXXV, 1998, pp. 807-847

Author(s)

Marco De Virgilis devirgilis.marco@gmail.com

References

Mack, T., Measuring the Variability of Chain Ladder Reserve Estimates, Casualty Actuarial Society Forum, Spring 1994