README.md

In senhu/mvClaim: Multivariate general insurance claims modelling

mvClaim R package

Multivariate general insurance claims modelling

Authors:

• Sen Hu ([e-mail])
• Thomas Brendan Murphy ([e-mail])
• Adrian O’Hagan ([e-mail])

Description

The mvClaim package provides a flexible modelling framework of mixture of experts (MoE) using bivariate gamma distributions, as introduced in Hu et al (2019). It implements the bivariate gamma distribution proposed by Cheriyan (1941) and Ramabhadran (1951), which has not received much attention in the past. Depends on the parameterization of the framework, its interpretation, and model parsimony issue, a family of models are implemented including:

• Bivariate gamma distribution estimation
• Bivariate gamma regression
• Mixture of bivariate gamma clustering
• Mixture of bivariate gamma regressions (i.e. mixture of bivariate gamma clustering with covariates)

The mvClaim package also provides a similar mixture model framework of finite mixture of copula regressions with gamma as marginal distribution, including

• Copula regression with gamma marginal distributions
• Mixture of copula regressions with gamma marginal distributions (i.e. mixture of copulas clustering with covariates)

Installation

You can install the latest development version of mvClaim from GitHub:

install.packages("devtools")
devtools::install_github("senhu/mvClaim")

Then the package can be loaded with:

library(mvClaim)

Bivariate Gamma MoE Example

This README file follows a package vignette format, and an example is briefly demonstrated using a simulated data set called gatingsim as illustrated in Hu et al (2019). The data were simulated based on a gating network MoE, i.e. covariates were used only in the gating network to assist with identifying which component the observation was from.

data("gatingsim")

First without considering covariates, assuming there is only one bivariate gamma distribution and no mixtures, the distribution parameters can be estimated via

dist.est <- BGE(gatingsim[,1:2])

Still without considering covariates, if assuming that the data are a mixture of two bivariate gamma distributions, there are three model types within this bivariate gamma MoE family: “CC”, “CI” and “IC”. Suppose the model type is “CC”, the mixture model can be fitted via:

mod1 <- MBGC(modelName = "CC", y=c("y1","y2"),
             G=2, gating = "C", data=gatingsim)

When taking covariates into consideration, we know the true data generating process for the data set gatingsim, based on which the optimal model can be fitted via

mod2 <- MBGC(modelName = "CC", y=c("y1","y2"),
             G=2, gating = ~w1+w2+w3, data=gatingsim)

In cases when covariates enter all gating and expert networks such as the case of the artificial data set fullsim, a model can be fitted via

mod3 <- MBGR(modelName = "VV", y=c("y1","y2"),
             G=2, data = fullsim,
             f1     = ~ w1 + w2 + w3,
             f2     = ~ w1 + w2 + w3,
             f3     = ~ w1 + w2 + w3,
             f4     = ~ w1 + w2 + w3,
             gating = ~ w1 + w2 + w3)

In such cases, there are 9 different model types: “VC”, “VI”, “VV”, “VE”, “CV”, “IV”, “EV”, “EC”, “CE”. Typically model selection issue needs to be addressed if the true model is unknown. We recommend a stepwise forward selection starting from a null model, i.e. fitting one bivariate gamma distribution without covariates. More details can be found in Hu et al (2019).

Mixture of Copula Regressions Example

Another example is briefly demonstrated here using a simulated data set called simdat.mcgr as illustrated in Hu and O’Hagan (2019). The data were simulated based on a mixture of two copula regressions, i.e. covariates were used to estimate the marginal distributions to assist the mixture of copulas estimation. Details of the sample data simulation process can be found in Hu and O’Hagan (2019).

data("simdat.mcgr")

Because we know the true data generating process for the data set simdat.mcgr, based on which the model can be fitted via

mod4 <- MCGR(copula = list(gumbelCopula(dim=2), frankCopula(dim=2)),
             f1 = y1 ~ x1+x2,
             f2 = y2 ~ x1+x2,
             G = 2,
             gating = "C"
             data=simdat.mcgr)

If G=1, as an alternative, copula regression with gamma marginals can be fitted via, for example:

mod5 <- copreg.gamma(f1 = y1 ~ x1+x2,
                     f2 = y2 ~ x1+x2,
                     copula = gumbelCopula(dim=2),
                     data = simdat.mcgr)

Reference

1. Hu, S., Murphy, T. B. and O’Hagan, A. (2019) Bivariate Gamma Mixture of Experts Models for Joint Claims Modeling. To appear.

2. Hu, S. and O’Hagan, A. (2019) Copula Averaging for Tail Dependence in General Insurance Claims Data. To appear.

senhu/mvClaim documentation built on Jan. 29, 2022, 3:18 p.m.