Some Mathematical Aspects of Price Optimisation

TL;DR

This paper explores mathematical methods for calculating optimal renewal insurance tariffs, addressing challenges in constructing tariffs under constraints and allocating premium loadings, with algorithmic solutions and simulations.

Contribution

It introduces mathematical frameworks and algorithmic approaches for optimal renewal tariff calculation in insurance, considering constraints and loadings.

Findings

Optimal tariffs can be constructed using continuous and discrete optimization methods.

Algorithmic solutions provide practical sub-optimal approaches to complex tariff problems.

Simulation techniques help illustrate the complexity and importance of optimization in insurance pricing.

Abstract

Calculation of an optimal tariff is a principal challenge for pricing actuaries. In this contribution we are concerned with the renewal insurance business discussing various mathematical aspects of calculation of an optimal renewal tariff. Our motivation comes from two important actuarial tasks, namely a) construction of an optimal renewal tariff subject to business and technical constraints, and b) determination of an optimal allocation of certain premium loadings. We consider both continuous and discrete optimisation and then present several algorithmic sub-optimal solutions. Additionally, we explore some simulation techniques. Several illustrative examples show both the complexity and the importance of the optimisation approach.