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PreprintCited by 5

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Discrimination-Free Insurance Pricing

Lindholm, Mathias, Richman, Ronald, Tsanakas, Andreas, Wuthrich, Mario V.·2020
DOI 10.2139/ssrn.3520676
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Abstract

A simple formula for non-discriminatory insurance pricing is introduced. This formula is based on the assumption that certain individual (discriminatory) policyholder information is not allowed to be used for insurance pricing. The suggested procedure can be summarized as follows: First, we construct a price that is based on all available information, including discriminatory information. Thereafter, we average out the effect of discriminatory information. This averaging out is done such that discriminatory information can also not be inferred from the remaining non-discriminatory one, thus, neither allowing for direct nor for indirect discrimination.

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Figures

FIGURE 1 (left) Causal diagram described by G ; (right) causal diagram altered according to the intervention X = x .
FIGURE 1 (left) Causal diagram described by G ; (right) causal diagram altered according to the intervention X = x .CC-BY · From the PDF
FIGURE 2 True model: (left) smokers and (right) non-smokers with solid black and red lines giving the best-estimate prices for women and men, respectively. The dotted orange lines show the discrimination-free prices and the dotted blue lines show the unawareness prices.
FIGURE 2 True model: (left) smokers and (right) non-smokers with solid black and red lines giving the best-estimate prices for women and men, respectively. The dotted orange lines show the discrimination-free prices and the dotted blue lines show the unawareness prices.CC-BY · From the PDF
FIGURE 3 True model: (left) smokers and (right) non-smokers with solid black and red lines giving the best-estimate prices for women and men, respectively. The dotted orange lines show the discrimination-free prices and the dotted green lines show the unawareness prices, for an alternative assumption on P ( D = woman | smoker).
FIGURE 3 True model: (left) smokers and (right) non-smokers with solid black and red lines giving the best-estimate prices for women and men, respectively. The dotted orange lines show the discrimination-free prices and the dotted green lines show the unawareness prices, for an alternative assumption on P ( D = woman | smoker).CC-BY · From the PDF
FIGURE 4 The age frequency used for both genders and smoking habits to simulate the data.
FIGURE 4 The age frequency used for both genders and smoking habits to simulate the data.CC-BY · From the PDF
FIGURE 5 Estimated regression functions ̂ λ 1 ( X , D ) (left), ̂ λ 2 ( X , D ) (middle), and ̂ λ 3 ( X , D ) (right) using the neural network architecture of Listing 2.
FIGURE 5 Estimated regression functions ̂ λ 1 ( X , D ) (left), ̂ λ 2 ( X , D ) (middle), and ̂ λ 3 ( X , D ) (right) using the neural network architecture of Listing 2.CC-BY · From the PDF
FIGURE 6 Estimated neural network model: (left) smokers and (right) non-smokers with solid black and red lines giving the best-estimate prices for women and men, respectively. The dotted orange lines show the discrimination-free prices and the dotted blue lines show the unawareness prices.
FIGURE 6 Estimated neural network model: (left) smokers and (right) non-smokers with solid black and red lines giving the best-estimate prices for women and men, respectively. The dotted orange lines show the discrimination-free prices and the dotted blue lines show the unawareness prices.CC-BY · From the PDF
FIGURE 7 Estimated regression functions ̂ λ 1 ( X ) (left), ̂ λ 2 ( X ) (middle), and ̂ λ 3 ( X ) (right) using neural networks and ignoring the gender information D .
FIGURE 7 Estimated regression functions ̂ λ 1 ( X ) (left), ̂ λ 2 ( X ) (middle), and ̂ λ 3 ( X ) (right) using neural networks and ignoring the gender information D .CC-BY · From the PDF
FIGURE 8 GLMestimated regression functions ̂ λ GLM 1 ( X , D ) (left), ̂ λ GLM 2 ( X , D ) (middle) and ̂ λ GLM 3 ( X , D ) (right).
FIGURE 8 GLMestimated regression functions ̂ λ GLM 1 ( X , D ) (left), ̂ λ GLM 2 ( X , D ) (middle) and ̂ λ GLM 3 ( X , D ) (right).CC-BY · From the PDF
FIGURE 9 Estimated GLM: (left) smokers and (right) non-smokers with solid black and red lines giving the best-estimate prices for women and men, respectively. The dotted orange lines show the discrimination-free prices and the dotted blue lines show the unawareness prices.
FIGURE 9 Estimated GLM: (left) smokers and (right) non-smokers with solid black and red lines giving the best-estimate prices for women and men, respectively. The dotted orange lines show the discrimination-free prices and the dotted blue lines show the unawareness prices.CC-BY · From the PDF
FIGURE 10 Bias-corrected discrimination-free prices ̂ h ∗ ( x ) against unadjusted discrimination-free prices h ( x ).
FIGURE 10 Bias-corrected discrimination-free prices ̂ h ∗ ( x ) against unadjusted discrimination-free prices h ( x ).CC-BY · From the PDF

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Citations

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Metadata

Authors
Lindholm, M., Richman, R., Tsanakas, A., & Wuthrich, M. V.
ORCID
Tsanakas, Andreas
Publisher
Elsevier BV
Published
2020
DOI
10.2139/ssrn.3520676
Cited by
5
References
0
Type
Preprint

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Lindholm, M., Richman, R., Tsanakas, A., & Wuthrich, M. V. (2020). Discrimination-Free Insurance Pricing. https://doi.org/10.2139/ssrn.3520676

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