hierCredibility() R function from [actuaRE]

Hierarchical credibility model of Jewell

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


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.

Returns

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.

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)

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

hierCredibility function

Hierarchical credibility model of Jewell

Arguments

Returns

Examples

References

See Also