Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Balance and Fairness through Multicalibration in Nonlife Insurance Pricing

Michel Denuit, Marie Michaelides, Julien Trufin

Abstract

Autocalibration is known to be an important requirement for insurance premiums since it guarantees that premium income balances corresponding claims, on average, not only at portfolio level but also inside each group paying similar premiums. Also, fairness has become a major concern because unfair treatment may expose insurers to lawsuits or reputational damage. Translating fairness into conditional mean independence allows actuaries to combine autocalibration and fairness into the multicalibration concept. This paper studies the properties of multicalibration in an insurance context and proposes practical ways to implement it, through local regression or bias correction within groups including credibility adjustments. A case study based on motor insurance data illustrates the relevance of multicalibration in insurance pricing.

Balance and Fairness through Multicalibration in Nonlife Insurance Pricing

Abstract

Autocalibration is known to be an important requirement for insurance premiums since it guarantees that premium income balances corresponding claims, on average, not only at portfolio level but also inside each group paying similar premiums. Also, fairness has become a major concern because unfair treatment may expose insurers to lawsuits or reputational damage. Translating fairness into conditional mean independence allows actuaries to combine autocalibration and fairness into the multicalibration concept. This paper studies the properties of multicalibration in an insurance context and proposes practical ways to implement it, through local regression or bias correction within groups including credibility adjustments. A case study based on motor insurance data illustrates the relevance of multicalibration in insurance pricing.
Paper Structure (32 sections, 3 theorems, 63 equations, 2 figures, 3 tables)

This paper contains 32 sections, 3 theorems, 63 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction and motivation
  2. Nonlife insurance pricing
  3. Autocalibration
  4. Fairness notion
  5. Sensitive feature
  6. Sufficiency
  7. Multicalibration
  8. Definition
  9. Properties
  10. Multibalance correction
  11. Practical implementation of multicalibration
  12. Categorical sensitive feature
  13. Direct empirical multibalance correction via groupwise regression
  14. Regularized empirical enforcement of multicalibration via iterative bias correction
  15. Binning and residual biases.
  16. ...and 17 more sections

Key Result

Proposition 6.2

The multibalance-corrected version $\pi_{\mathrm{mbc}}(\cdot)$ of the premium $\pi(\cdot)$ defined in DefMBC is multicalibrated with respect to $S=X_{j_0}$.

Figures (2)

  • Figure 7.1: Mean residual pricing bias across premium bins for discrete vehicle-age groups. Top row: baseline vs. autocalibration. Middle row: autocalibration via iterative algorithm (left) and balance correction via isotonic regression (right). Bottom row: multicalibration (iterative) and multibalance correction (group-wise isotonic regression).
  • Figure 7.2: Mean residual pricing bias across premium bins for continuous vehicle-age. Top row: baseline vs. autocalibration. Middle row: autocalibration via iterative algorithm (left) and balance correction via isotonic regression (right). Bottom row: multicalibration (iterative) and multibalance correction (groupwise isotonic regression).

Theorems & Definitions (16)

  • Definition 3.1
  • Example 4.1
  • Remark 4.2
  • Remark 4.3
  • Definition 4.4
  • Definition 5.1
  • proof
  • proof
  • Definition 6.1
  • Proposition 6.2
  • ...and 6 more