Fit Chain Ladder Plus to reverse time triangles. — clmplus.AggregateDataPP • clmplus

Method to fit Chain Ladder plus models to AggregateDataPP objects.

Usage

# S3 method for class 'AggregateDataPP'
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

An object of class clmplusmodel. A list with the following elements:

model.fit: fitStMoMo object, specified hazard model fit from StMoMo.
apc_input: list object. A list containing the following model inputs in age-period-cohort notation: J (integer) Run-off triangle dimension. eta (numeric) Expected time-to-event in the cell. I.e., lost exposure. diagonal (numeric) Cumulative payments last diagonal. hazard.model (character), hazard model specified from the user. Set to user.specific when a custom model is passed.
hazard_scaled_deviance_residuals: matrix array Triangle of the scaled deviance residuals.
fitted_development_factors: matrix array Triangle of the fitted development factors.
fitted_effects: list List of the development-accident-calendar effects fitted.

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 weighted: 1 
#> StMoMo: The following years have been zero weighted: 1 
#> StMoMo: The following cohorts have been zero weighted: -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