Defining and estimating stochastic rate change in a dynamic general insurance portfolio

TL;DR

This paper introduces a stochastic definition of rate change in insurance portfolios, emphasizing estimation of its population parameter using matched sampling and optimization techniques to improve accuracy over traditional deterministic methods.

Contribution

It proposes a new stochastic framework for rate change, utilizing matched sampling and genetic algorithms to better estimate and understand rate dynamics in insurance portfolios.

Findings

Matched sampling effectively adjusts for policy characteristic changes.

Genetic algorithms optimize the matching process.

Application to motor insurance data demonstrates practical utility.

Abstract

Rate change calculations in the literature involve deterministic methods that measure the change in premium for a given policy. The definition of rate change as a statistical parameter is proposed to address the stochastic nature of the premium charged for a policy. It promotes the idea that rate change is a property of an asymptotic population to be estimated, not just a property to measure or monitor in the sample of observed policies that are written. Various models and techniques are given for estimating this stochastic rate change and quantifying the uncertainty in the estimates. The use of matched sampling is emphasized for rate change estimation, as it adjusts for changes in policy characteristics by directly searching for similar policies across policy years. This avoids any of the assumptions and recipes that are required to re-rate policies in years where they were not written, as is common with deterministic methods. Such procedures can be subjective or implausible if the structure of rating algorithms change or there are complex and heterogeneous exposure bases and coverages. The methods discussed are applied to a motor premium database. The application includes the use of a genetic algorithm with parallel computations to automatically optimize the matched sampling.