CLFMdelta: Find "selection consistent" values of delta In edalmoro/ChainLadderQuantileV1: Statistical Methods and Models for Claims Reserving in General Insurance

Description

This function finds the values of delta, one for each development period, such that the model coefficients resulting from the 'chainladder' function with delta = solution are consistent with an input vector of 'selected' development age-to-age factors.

Usage

 `1` ```CLFMdelta(Triangle, selected, tolerance = .0005, ...) ```

Arguments

 `Triangle` cumulative claims triangle. 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
 `...` not in use

Details

For a given input Triangle and vector of selected factors, a search is conducted for chainladder models that are "consistent with" the selected factors. By "consistent with" is meant that the coefficients of the `chainladder` function are equivalent to the selected factors. Not all vectors of selected factors can be considered consistent with a given Triangle; feasibility is subject to restrictions on the 'selected' factors relative to the input 'Triangle'. See the References.

The default average produced by the `chainladder` function is the volume weighted average and corresponds to `delta = 1` in the call to that function; `delta = 2` produces the simple average; and `delta = 0` produces the "regression average", i.e., the slope of a regression line fit to the data and running through the origin. By convention, if the `selected` value corresponds to the volume-weighted average, the simple average, or the regression average, then the value returned will be 1, 2, and 0, respectively.

Other real-number values for `delta` will produce a different average. The point of this function is to see if there exists a model as determined by delta whose average is consistent with the value in the `selected` vector. That is not always possible. See the References.

It can be the case that one or more of the above three "standard averages" will be quite close to each other (indistinguishable within `tolerance`). In that case, the value returned will be, in the following priority order by convention, 1 (volume weighted average), 2 (simple average), or 0 (regression average).

Value

A vector of real numbers, say delta0, such that `coef(chainladder(Triangle, delta = delta0))` = `selected` within `tolerance`. A `logical` attribute 'foundSolution' indicates if a solution was found for each element of `selected`.

Dan Murphy

References

Bardis, Majidi, Murphy. A Family of Chain-Ladder Factor Models for Selected Link Ratios. Variance. Pending. Variance 6:2, 2012, pp. 143-160. http://www.variancejournal.org/issues/06-02/143.pdf

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```x <- RAA[1:9,1] y <- RAA[1:9,2] F <- y/x CLFMdelta(RAA[1:9, 1:2], selected = mean(F)) # value is 2, 'foundSolution' is TRUE CLFMdelta(RAA[1:9, 1:2], selected = sum(y) / sum(x)) # value is 1, 'foundSolution' is TRUE selected <- mean(c(mean(F), sum(y) / sum(x))) # an average of averages CLFMdelta(RAA[1:9, 1:2], selected) # about 1.725 CLFMdelta(RAA[1:9, 1:2], selected = 2) # negative solutions are possible # Demonstrating an "unreasonable" selected factor. CLFMdelta(RAA[1:9, 1:2], selected = 1.9) # NA solution, with warning ```

edalmoro/ChainLadderQuantileV1 documentation built on Oct. 1, 2018, 12:23 a.m.