Pricing insurance policies with offsetting relationship

TL;DR

This paper explores how incorporating diversification effects in joint insurance policy pricing can offer competitive advantages, modeling relationships between premiums and customer numbers, and validating findings with Brazilian market data.

Contribution

It introduces a model for joint insurance pricing considering diversification benefits and customer sensitivity, with empirical validation using real market data.

Findings

Joint pricing can be advantageous despite underwriting constraints.

Optimal pricing depends on policyholders' price sensitivity.

Most policy pairs are suitable for joint pricing even with high correlations.

Abstract

This paper investigates the benefits of incorporating diversification effects into the pricing process of insurance policies from two different business lines. The paper shows that, for the same risk reduction, insurers pricing policies jointly can have a competitive advantage over those pricing them separately. However, the choice of competitiveness constrains the underwriting flexibility of joint pricers. The paper goes a step further by modeling explicitly the relationship between premiums and the number of customers in each line. Using the total collected premiums as a criterion to compare the competing strategies, the paper provides conditions for the optimal pricing decision based on policyholders' sensitivity to price discounts. The results are illustrated for a portfolio of annuities and assurances. Further, using non-life data from the Brazilian insurance market, an empirical exploration shows that most pairs satisfy the condition for being priced jointly, even when pairwise correlations are high.