Robust and Pareto Optimality of Insurance Contracts

European Journal of Operational Research, 262(2), pp. 720–732. doi:10.1016/j.ejor.2017.04.029.

32 Pages Posted: 3 Sep 2016 Last revised: 8 Feb 2018

See all articles by Alexandru Vali Asimit

Alexandru Vali Asimit

Cass Business School, City, University of London

Valeria Bignozzi

Università di Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Ka Chun Cheung

The University of Hong Kong

Junlei Hu

University of Essex

Eun-Seok Kim

Queen Mary, University of London

Date Written: April 27, 2017

Abstract

The optimal insurance problem represents a fast growing topic that explains the most efficient contract that an insurance player may get. The classical problem investigates the ideal contract under the assumption that the underlying risk distribution is known, i.e. by ignoring the parameter and model risks. Taking these sources of risk into account, the decision-maker aims to identify a robust optimal contract that is not sensitive to the chosen risk distribution. We focus on Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR)-based decisions, but further extensions for other risk measures are easily possible. The Worst-case scenario and Worst-case regret robust models are discussed in this paper, which have been already used in robust optimisation literature related to the investment portfolio problem. Closed-form solutions are obtained for the VaR Worst-case scenario case, while Linear Programming (LP) formulations are provided for all other cases. A caveat of robust optimisation is that the optimal solution may not be unique, and therefore, it may not be economically acceptable, i.e. Pareto optimal. This issue is numerically addressed and simple numerical methods are found for constructing insurance contracts that are Pareto and robust optimal. Our numerical illustrations show weak evidence in favour of our robust solutions for VaR-decisions, while our robust methods are clearly preferred for CVaR-based decisions.

Keywords: Uncertainty modelling, Linear programming, Robust/Pareto optimal insurance, Risk measure, Robust optimisation

JEL Classification: C18, C61, D81, G22

Suggested Citation

Asimit, Alexandru Vali and Bignozzi, Valeria and Cheung, Ka Chun and Hu, Junlei and Kim, Eun-Seok, Robust and Pareto Optimality of Insurance Contracts (April 27, 2017). European Journal of Operational Research, 262(2), pp. 720–732. doi:10.1016/j.ejor.2017.04.029., Available at SSRN: https://ssrn.com/abstract=2834079 or http://dx.doi.org/10.2139/ssrn.2834079

Alexandru Vali Asimit (Contact Author)

Cass Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Valeria Bignozzi

Università di Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Via Bicocca degli Arcimboldi, 8
Milano, 20126
Italy

Ka Chun Cheung

The University of Hong Kong ( email )

Pokfulam Road
Hong Kong, Pokfulam HK
China

Junlei Hu

University of Essex ( email )

Wivenhoe Park
Colchester, Essex CO4 3SQ
United Kingdom

Eun-Seok Kim

Queen Mary, University of London ( email )

Mile End Rd
Mile End Road
London, London E1 4NS
United Kingdom

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