B1264
Title: Robust and Pareto optimality of insurance contracts
Authors: Vali Asimit - City University London (United Kingdom) [presenting]
Valeria Bignozzi - University of Rome Sapienza (Italy)
Ka Chun Cheung - The University of Hong Kong (Hong Kong)
Junlei Hu - City University LOndon (United Kingdom)
Eun-Seok Kim - Middlesex University (United Kingdom)
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 are easily possible. The worst-case scenario and worst-case regret robust models are discussed, which have been already used in the investment portfolio literature. Closed-form solutions are obtained for the VaR Worst-case scenario case, while Linear Programming (LP) formulations are provided for all other cases. The Pareto optimality of the robust insurance contracts is also investigated and simple numerical methods are found for constructing insurance contracts that are Pareto and robust optimal. Our numerical illustrations have shown that marginal evidence in favour of our robust solutions is obtained for VaR-decisions, while our robust methods are clearly preferred for all other risk measures.
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