hierCredibility {actuaRE}

Hierarchical credibility model of Jewell

Description

Fit a random effects model, without contract-specific risk factors, using the hierarchical credibility model of Jewell.

Usage

hierCredibility(
  Yijkt,
  wijkt,
  sector,
  group,
  data,
  muHat = NULL,
  type = c("additive", "multiplicative"),
  returnData = FALSE
)

Arguments

Yijkt

variable name of the response variable (the loss cost within actuarial applications).

wijkt

variable name of the exposure weight.

sector

variable name of the first hierarchical level.

group

variable name of the second hierarchical level that is nested within the first hierarchical level.

data

an object that is coercible by as.data.table, containing the variables in the model.

muHat

estimate for the intercept term. Default is NULL and in this case, the estimator as given in Ohlsson (2005) is used.

type

specifies whether the additive (Dannenburg, 1996) or multiplicative (Ohlsson, 2005) formulation of the hierarchical credibility model is used. Default is additive.

returnData

Logical, indicates whether the data object has to be returned. Default is FALSE.

Value

An object of type hierCredibility with the following slots:

call

the matched call

type

Whether additive or multiplicative hierarchical credibility model is used.

Variances

The estimated variance components. s2 is the estimated variance of the individual contracts, tausq the estimate of Var(V[j]) and nusq is the estimate of Var(V[jk]).

Means

The estimated averages at the portfolio level (intercept term \mu), at the first hierarchical level (bar(Y)[\%.\% j \%.\% \%.\%]^z) and at the second hierarchical level (bar(Y)[\%.\% jk \%.\%]).

Weights

The weights at the first hierarchical level z[j\%.\%] and at the second hierarchical level w[\%.\%jk\%.\%].

Credibility

The credibility weights at the first hierarchical level q[j\%.\%] and at the second hierarchical level z[jk].

Premiums

The overall expectation widehat(\mu), sector expectation widehat(V)[j] and group expectation widehat(V)[jk].

Relativity

The estimated random effects widehat(U)[j] and widehat(U)[jk] of the sector and group, respectively.

RawResults

Objects of type data.table with all intermediate results.

fitted.values

the fitted mean values, resulting from the model fit.

References

Campo, B.D.C. and Antonio, Katrien (2023). Insurance pricing with hierarchically structured data an illustration with a workers' compensation insurance portfolio. Scandinavian Actuarial Journal, doi: 10.1080/03461238.2022.2161413

Dannenburg, D. R., Kaas, R. and Goovaerts, M. J. (1996). Practical actuarial credibility models. Amsterdam: IAE (Institute of Actuarial Science and Econometrics of the University of Amsterdam).

Jewell, W. S. (1975). The use of collateral data in credibility theory: a hierarchical model. Laxenburg: IIASA.

Ohlsson, E. (2005). Simplified estimation of structure parameters in hierarchical credibility. Presented at the Zurich ASTIN Colloquium.http://www.actuaries.org/ASTIN/Colloquia/Zurich/Ohlsson.pdf

See Also

hierCredibility-class, fitted.hierCredibility, predict.hierCredibility, ranef-actuaRE, weights-actuaRE, hierCredTweedie, hierCredGLM, cpglm, plotRE

Examples

library(actuar)
library(actuaRE)
data("hachemeister", package = "actuar")
Df = as.data.frame(hachemeister)
X  = as.data.frame(cbind(cohort = c(1, 2, 1, 2, 2), hachemeister))
Df = reshape(X, idvar = "state", varying = list(paste0("ratio.", 1:12),
 paste0("weight.", 1:12)), direction = "long")
fitActuar  = cm(~ cohort + cohort:state, data = X, ratios = ratio.1:ratio.12,
weights = weight.1:weight.12, method = "Ohlsson")
fitActuaRE = hierCredibility(ratio.1, weight.1, cohort, state, Df)
summary(fitActuar)
summary(fitActuaRE)