Some Mathematical Aspects of Price Optimisation

24 Pages Posted: 16 May 2016 Last revised: 22 Jul 2017

See all articles by Enkelejd Hashorva

Enkelejd Hashorva

University of Lausanne, Actuarial Department

Gildas Ratovomirija

University of Lausanne

Maissa Tamraz

Universite de Lausanne; Nankai University

Yizhou Bai

University of Lausanne

Date Written: May 12, 2016

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.

Keywords: Market Tariff; Optimal Tariff; Optimal Price; Price Elasticity; Non-Life Insurance; Non-Convex Opti- Misation; Quadratic Programming; Sequential Quadratic Programming; Mixed Discrete Non-Linear Programming; Constraints; Renewal Busines

JEL Classification: C64; G22

Suggested Citation

Hashorva, Enkelejd and Ratovomirija, Gildas and Tamraz, Maissa and Bai, Yizhou, Some Mathematical Aspects of Price Optimisation (May 12, 2016). Available at SSRN: https://ssrn.com/abstract=2779334 or http://dx.doi.org/10.2139/ssrn.2779334

Enkelejd Hashorva

University of Lausanne, Actuarial Department ( email )

Unil Dorigny, Batiment Internef
Lausanne, 1015
Switzerland

Gildas Ratovomirija (Contact Author)

University of Lausanne ( email )

Unil-Dorigny
Vaud
Lausanne, Vaud 1015
Switzerland

Maissa Tamraz

Universite de Lausanne ( email )

Lausanne, 1015
Switzerland

Nankai University

94 Weijin Road
Tianjin, 300071
China

Yizhou Bai

University of Lausanne ( email )

Lausanne, Vaud CH-1015
Switzerland

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