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Robust and Pareto optimality of insurance contracts

Asimit, Alexandru V and Bignozzi, Valeria and Cheung, Ka Chun and Hu, Junlei and Kim, Eun-Seok (2017) 'Robust and Pareto optimality of insurance contracts.' European Journal of Operational Research, 262 (2). 720 - 732. ISSN 0377-2217

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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.

Item Type: Article
Uncontrolled Keywords: Uncertainty modelling, Linear programming, Robust/Pareto optimal insurance, Risk measure, Robust optimisation
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 17 Jan 2020 15:48
Last Modified: 17 Jan 2020 15:48
URI: http://repository.essex.ac.uk/id/eprint/26500

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