Title: Defining and estimating stochastic rate change in a dynamic general insurance portfolio,
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.