Accident and Development Period Adjusted Linear Pools for Actuarial Stochastic Reserving

Loss reserving generally focuses on identifying a single model that can generate superior predictive performance. However, different loss reserving models specialise in capturing different aspects of loss data. This is recognised in practice in the sense that results from different models are often considered, and sometimes combined. For instance, actuaries may take a weighted average of the prediction outcomes from various loss reserving models, often based on subjective assessments. This package allows for the use of a systematic framework to objectively combine (i.e. ensemble) multiple stochastic loss reserving models such that the strengths offered by different models can be utilised effectively. Our framework is developed in Avanzi et al. (2023). Firstly, our criteria model combination considers the full distributional properties of the ensemble and not just the central estimate - which is of particular importance in the reserving context. Secondly, our framework is that it is tailored for the features inherent to reserving data. These include, for instance, accident, development, calendar, and claim maturity effects. Crucially, the relative importance and scarcity of data across accident periods renders the problem distinct from the traditional ensemble techniques in statistical learning. Our framework is illustrated with a complex synthetic dataset. In the results, the optimised ensemble outperforms both (i) traditional model selection strategies, and (ii) an equally weighted ensemble. In particular, the improvement occurs not only with central estimates but also relevant quantiles, such as the 75th percentile of reserves (typically of interest to both insurers and regulators). Reference: Avanzi B, Li Y, Wong B, Xian A (2023) "Ensemble distributional forecasting for insurance loss reserving" .

ADLP

Repository for ADLP - ensemble reserving package

Introduction

We present ADLP (Accident and Development period adjusted Linear Pools), a tailored ensemble technique for general insurance loss reserving. ADLP seeks to combine various loss reserving models, leveraging their strengths, with combination weights optimised to enhance the ensemble's distributional forecasting performance.

This package originates from the paper "Ensemble distributional forecasting for insurance loss reserving," while also offering users ample flexibility to choose or create component models for the ensemble, and to employ data partitioning for calibrating either the component models or the combination weights, aligning with their experiences.

Package Overview

This section provides an overview of the folders and files located in this repository; their purposes will also be briefly introduced.

• R: stores the sources of R codes used in constructing the package functions.
  • train_val_split.R
    • Defines the functions for partitioning the claims triangle into training and validation sets.
  • components.R
    • Defines the functions for storing the component models used in the ensemble, and functions for calculating the density, mean, and cumulative distribution of the component models. The simulation function for component models is also contained.
  • custom_model.R:
    • Defines the functions to build customised models.
  • partitions.R:
    • Defines the functions to partition the data used for calibrating the ensemble weights.
  • mm_optim.R:
    • Defines the functions to optimise the ensemble weights based on the Minorisation-Maximisation (MM) algorithm.
  • adlp.R:
    • Defines the functions to calibrate an ADLP ensemble, and functions to calculate the density, Log Score and CRPS of the fitted ADLP objects. The simulation function for ADLP ensembles is also contained.
  • S3_methods.R:
    • Contains miscellaneous functions used for predictions and results printing.
• vignettes: contains the demonstration file for the ADLP package (ADLP-demo.Rmd).

Reference

For a full description of ADLP's structure and modelling details, readers should refer to:

Avanzi, B., Li, Y., Wong, B., & Xian, A. (2022). Ensemble distributional forecasting for insurance loss reserving. arXiv preprint arXiv:2206.08541.

To cite this package in publications, please use:

citation("ADLP")

Install Package

To install the development version of the package from this GitHub repository, do

if (!require(remotes)) install.packages("remotes")
remotes::install_github("agi-lab/ADLP/ADLP-package", build_vignettes = TRUE)

After the installation, run:

library(ADLP)

as you would normally do will load the package. View a full demonstration of the package by running

vignette("ADLP-demo", package = "ADLP")