# OptiGrad: A Fair and more Efficient Price Elasticity Optimization via a Gradient Based Learning

**Authors:** Vincent Grari, Marcin Detyniecki  
**arXiv:** [2404.10275](https://arxiv.org/abs/2404.10275)  
**Date:** 2024-04-16  
**Summary page:** https://www.summarizepaper.com/en/paper/2404.10275v1/

## Key points

- Authors Vincent Grari and Marcin Detyniecki introduce OptiGrad method for optimizing profit margins in non-life insurance markets
- Three primary objectives: maximizing profit margins, ensuring conversion rates, enforcing fairness criteria like demographic parity (DP)
- Traditional methods rely on linear and semi-definite programming, struggle with balancing profitability and fairness
- Indirect Ratebook optimization method uses predictor models but faces challenges in continuous rate scenarios
- Actuaries often use discrete intervals for optimization leading to approximate estimations and suboptimal pricing strategies
- Proposed method employs direct optimization in continuous rate space with adversarial predictor model for fairness enforcement
- Method reduces sequential errors, simplifies complexities of traditional models, integrates fairness measures directly into premium calculations
- Empirical demonstrations show improved margin performance and enhanced enforcement of fairness measures

## Summary

In their paper titled "OptiGrad: A Fair and more Efficient Price Elasticity Optimization via a Gradient Based Learning," authors Vincent Grari and Marcin Detyniecki introduce a groundbreaking method for optimizing profit margins in non-life insurance markets. The approach focuses on three primary objectives: maximizing profit margins, ensuring conversion rates, and enforcing fairness criteria such as demographic parity (DP). Traditional pricing optimization methods heavily rely on linear and semi-definite programming, which often struggle to strike a balance between profitability and fairness, especially in scenarios requiring continuous rate adjustments and the integration of fairness criteria. The widely-used indirect Ratebook optimization method for setting prices for new business utilizes predictor models like XGBoost or GLMs/GAMs to estimate individually optimized prices downstream. However, this strategy is susceptible to sequential errors and faces challenges in managing optimizations for continuous rate scenarios effectively. Actuaries frequently opt for optimization within discrete intervals (e.g., range of [-20\%, +20%] with fixed increments) to save time, leading to approximate estimations. Additionally, they may relax constraints to avoid infeasible solutions, resulting in suboptimal pricing strategies. The reverse-engineered nature of traditional models further complicates the enforcement of fairness criteria, potentially leading to biased outcomes. To address these challenges, the proposed method employs a direct optimization strategy in the continuous space of rates while embedding fairness through an adversarial predictor model. This innovative approach not only reduces sequential errors and simplifies complexities present in traditional models but also integrates fairness measures directly into commercial premium calculations. Through empirical demonstrations, the authors showcase improved margin performance and enhanced enforcement of fairness measures, underscoring the critical necessity to evolve existing pricing strategies in non-life insurance markets.