Author: Robert Matthijs Verschuren
Institution: Amsterdam School of Economics, University of Amsterdam
The aim of this paper is to explore how to best account for customers' price sensitivity in (multi-period) renewal optimization in non-life insurance. The frameworks introduced rely on causal inference and are applied to a Dutch automobile insurance portfolio with three years of data. My findings suggest that a policy’s competitiveness in the market is crucial for a customer’s price sensitivity and enables temporal feedback of previous rate changes on future demand. Moreover, both frameworks indicate that substantially more profit can be gained on the portfolio than realized, also already with less churn and in particular in the approach with continuous treatments.
The causal inference frameworks introduced in this paper are applied to a confidential automobile insurance portfolio from a large Dutch insurer. More specifically, it contains the risk and renewal characteristics of individual policy renewals on automobile insurance in the period of 2017 up to and including 2019. This portfolio additionally contains the premia offered by six of the largest competitors in the market for each policy renewal.
The relevant R code for performing the causal inference approaches is provided in the 7-Zip file Supplementary code - Verschuren, R. M. (2022).7z. To begin with, the two (generalized) propensity score matching algorithms are provided in the folder "Propensity_score_matching" and are denoted by A = Discrete for the discrete treatment approach and by A = Continuous in the continuous treatment approach in the files Matching_A.R. In the files Matching_A_B.R in this same folder the discrete (A = Discrete) and continuous (A = Continuous) approach are adjusted to accommodate 10, 20, 50, 100, 150 or 200 treatment intervals (B = Intervals) and random forests, neural networks, or GAMs (B = Alternative). After the matching procedure, the customer price sensitivities are estimated with the files Sensitivities_C.R in the folder "Customer_price_sensitivities", where C = {Discrete, Discrete_without_imputation, Discrete_XGBoost, Continuous} for the discrete approach with or without multiple imputation or with XGBoost, or the continuous approach, respectively. The corresponding efficient frontiers are determined in the folder "Efficient_frontier" and are denoted by D = {Discrete, Discrete_without_imputation, Discrete_XGBoost, Continuous, Continuous_restricted} in the files Frontier_D.R, where D = Continuous_restricted for the continuous approach restricted to the five categorical rate change medians. Finally, the folder "Multi_period_renewal_optimization" contains the multi-period analogue of the efficient frontiers, produced with the files Multi_period_D.R for D = {Discrete, Discrete_without_imputation, Discrete_XGBoost, Continuous, Continuous_restricted}. For more details on the theoretical and empirical results, we refer the reader to the paper of Verschuren, R. M. in Expert Systems with Applications.