Fit Chain Ladder plus on Run-off Triangles.

Method to Estimate Chain Ladder plus models.

Usage

clmplus(
  AggregateDataPP,
  hazard.model = NULL,
  link = c("log", "logit"),
  staticAgeFun = TRUE,
  periodAgeFun = "NP",
  cohortAgeFun = NULL,
  effect_log_scale = TRUE,
  constFun = function(ax, bx, kt, b0x, gc, wxt, ages) list(ax = ax, bx = bx, kt = kt, b0x
    = b0x, gc = gc),
  ...
)

Arguments

AggregateDataPP

AggregateDataPP object, reverse time triangle to be fitted.

hazard.model

character, hazard model supported from our package. The model can be chosen from:

'a': Age model, this is equivalent to the Mack chain-ladder.
'ac': Age and cohort effects.
'ap': Age and cohort effects.
'apc': Age cohort and period effects.

link

character, defines the link function and random component associated with the mortality model. "log" would assume that deaths follow a Poisson distribution and use a log link while "logit" would assume that deaths follow a Binomial distribution and a logit link. To be disregarded unless the practitioner specifies his own hazard model in StMoMo.

staticAgeFun

logical, indicates if a static age function \(\alpha_x\) is to be included. To be disregarded unless the practitioner specifies his own hazard model in StMoMo.

periodAgeFun

list, a list of length \(N\) with the definitions of the period age modulating parameters \(\beta_x^{(i)}\). Each entry can take values: "NP" for non-parametric age terms, "1" for \(\beta_x^{(i)}=1\) or a predefined parametric function of age (see details). Set this to NULL if there are no period terms in the model. To be disregarded unless the practitioner specifies his own hazard model in StMoMo.

cohortAgeFun

character or function, defines the cohort age modulating parameter \(\beta_x^{(0)}\). It can take values: "NP" for non-parametric age terms, "1" for \(\beta_x^{(0)}=1\), a predefined parametric function of age (see details) or NULL if there is no cohort effect. To be disregarded unless the practitioner specifies his own hazard model in StMoMo.

effect_log_scale

logical, whether effects should be on the logarithmic scale. By default, TRUE.

constFun

function, it defines the identifiability constraints of the model. It must be a function of the form constFun <- function(ax, bx, kt, b0x, gc, wxt, ages) taking a set of fitted model parameters and returning a list list(ax = ax, bx = bx, kt = kt, b0x = b0x, gc = gc) of the model parameters with the identifiability constraints applied. If omitted no identifiability constraints are applied to the model. To be disregarded unless the practitioner specifies his own hazard model in StMoMo.

...

parameters to be passed to clmplus.

Value

No return value, called to pass method clmplus.AggregateDataPP. See clmplus.AggregateDataPP documentation.

References

Pittarello, Gabriele, Munir Hiabu, and Andrés M. Villegas. "Replicating and extending chain ladder via an age-period-cohort structure on the claim development in a run-off triangle." arXiv preprint arXiv:2301.03858 (2023).

Examples

data(sifa.mtpl)
sifa.mtpl.rtt <- AggregateDataPP(cumulative.payments.triangle=sifa.mtpl)
hz.chl=clmplus(sifa.mtpl.rtt, 'a')
#> Warning: StMoMo: 66 missing values which have been zero weighted
#> StMoMo: The following ages have been zero weigthed: 1 
#> StMoMo: The following years have been zero weigthed: 1 
#> StMoMo: The following cohorts have been zero weigthed: -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 11 
#> StMoMo: Start fitting with gnm
#> Warning: non-integer x = 860.063891
#> Warning: non-integer x = 458.156066
#> Warning: non-integer x = 559.340054
#> Warning: non-integer x = 281.869679
#> Warning: non-integer x = 456.270650
#> Warning: non-integer x = 727.142070
#> Warning: non-integer x = 49353.589600
#> Warning: non-integer x = 50605.820000
#> Warning: non-integer x = 29251.193380
#> Warning: non-integer x = 36106.295210
#> Warning: non-integer x = 40125.390780
#> Warning: non-integer x = 44498.942240
#> Warning: non-integer x = 45490.189570
#> Warning: non-integer x = 48040.321560
#> Warning: non-integer x = 49991.357650
#> Warning: non-integer x = 49694.294990
#> Warning: non-integer x = 20880.666980
#> Warning: non-integer x = 18304.246140
#> Warning: non-integer x = 18603.713030
#> Warning: non-integer x = 12463.983790
#> Warning: non-integer x = 13441.333110
#> Warning: non-integer x = 12951.176400
#> Warning: non-integer x = 15370.423630
#> Warning: non-integer x = 15339.426370
#> Warning: non-integer x = 17842.901760
#> Warning: non-integer x = 19570.203660
#> Warning: non-integer x = 10047.067150
#> Warning: non-integer x = 8201.559214
#> Warning: non-integer x = 8833.487780
#> Warning: non-integer x = 5144.085289
#> Warning: non-integer x = 5868.234632
#> Warning: non-integer x = 6033.755464
#> Warning: non-integer x = 5593.853546
#> Warning: non-integer x = 5478.076757
#> Warning: non-integer x = 7035.199194
#> Warning: non-integer x = 3933.606063
#> Warning: non-integer x = 5749.890057
#> Warning: non-integer x = 4714.168250
#> Warning: non-integer x = 2726.947823
#> Warning: non-integer x = 2881.972323
#> Warning: non-integer x = 3009.655856
#> Warning: non-integer x = 2615.516340
#> Warning: non-integer x = 2540.639658
#> Warning: non-integer x = 2906.368627
#> Warning: non-integer x = 2725.682936
#> Warning: non-integer x = 3312.691467
#> Warning: non-integer x = 2359.362462
#> Warning: non-integer x = 2421.987896
#> Warning: non-integer x = 1264.396267
#> Warning: non-integer x = 1984.311792
#> Warning: non-integer x = 2136.804699
#> Warning: non-integer x = 1294.338023
#> Warning: non-integer x = 2266.599873
#> Warning: non-integer x = 1333.856105
#> Warning: non-integer x = 918.004039
#> Warning: non-integer x = 1249.952517
#> Warning: non-integer x = 1134.706143
#> Warning: non-integer x = 1184.355428
#> Warning: non-integer x = 1124.336355
#> Warning: non-integer x = 1238.429974
#> Warning: non-integer x = 1075.978340
#> Warning: non-integer x = 733.741025
#> Warning: non-integer x = 904.371165
#> Warning: non-integer x = 872.633331
#> Warning: non-integer x = 941.440475
#> StMoMo: Finish fitting with gnm