A unisex stochastic mortality model to comply with EU Gender Directive

Abstract

EU Gender Directive ruled out discrimination against gender in charging premium for insurance products. This prohibition prevents the use of the standard actuarial fairness principle to price life insurance products. According to current actuarial practice, unisex premiums are calculated with a simple weighting rule of the gender-specific life tables. This procedure is likely to violate portfolio fairness principles. Up to our knowledge, in the actuarial literature there is no unisex mortality model that respects the unisex fairness principle. This paper is the first attempt to fill this gap. First, we recall the notion of unisex fairness principle and the corresponding unisex fair premium. Then, we provide a unisex stochastic mortality model for the mortality intensity that is underlying the pricing of a life portfolio of females and males belonging to the same cohort. Finally, we calibrate the unisex mortality model using the unisex fairness principle. We find that the weighting coefficient between the males' and females' own mortalities depends mainly on the quote of portfolio relative to each gender, on the * We thank the participants to the 19th International Congress on Insurance: Mathematics and Economics and those to the 3rd European Actuarial Journal Conference for useful remarks. We are indebted to Paolo De Angelis, Kristian Buchardt, Montserrat Guillen, Elisa Luciano, Pietro Millossovich, Luca Regis and two anonymous referees for very valuable comments that improved the paper. age, and on the type of insurance product. The knowledge of a proper unisex mortality model could help life insurance companies to better understanding the nature of the risk of a mixed portfolio.

Solvency Requirement in a Unisex Mortality Model

“…In this section, we report the main results in Chen and Vigna (2017), recalling the definition of unisex fairness principle.…”

“…where τ := T − t. Chen and Vigna (2017) model the mortality intensity of a representative unisex policyholder of the mixed portfolio as a weighted average of the males' and females' mortality intensities, and provide the following definition.…”

“…Schmeiser et al (2014) discuss unisex insurance pricing also from the regulator's perspective and Thiery and Van Schoubroeck (2006) deal with the legal aspects of fairness and equality in actuarial risk selection. Chen and Vigna (2017) show how insurance companies can price a portfolio of policies issued to males and females of the same age if they want to respect actuarial fairness at the portfolio level, and they introduce the unisex mortality intensity that is in accordance with the fairness principle.…”

“…In the present paper, we investigate the implications of the adoption of the unisex fairness principle on the SCR, particularly the initial SCR. Taking pure endowments and life annuities as examples, we compute the initial SCR per policy relying on a single "unisex" portfolio and satisfying the initial actuarial fairness principle (Chen and Vigna, 2017), and we compare it with the weighted average of the gender-based per policy SCRs. For these life insurance contracts, we show that the SCR at issuing time of the mixed portfolio calculated with unisex survival probabilities is greater than the sum of the SCRs of the gender-based subportfolios.…”

How Do Unisex Life Care Annuities Embedded in a Pay-As-You-Go Retirement System Affect Gender Redistribution?

“…And fourth, in order to compute the gender-neutral actuarial factor, we follow the current practice in insurance companies (Chen & Vigna, 2017), which seems to be to calculate a unisex tariff obtained by mixing the life tables, in our case mortality and morbidity tables, for the two sexes (see Appendix 1). However, contrary to the usual practice in insurance, we have not introduced a correction giving more weight to the table for the high-risk gender (females).…”