Optimal Robust Insurance with a Finite Uncertainty Set

32 Pages Posted: 29 Jan 2018 Last revised: 31 Mar 2019

See all articles by Alexandru Vali Asimit

Alexandru Vali Asimit

Cass Business School, City, University of London

Junlei Hu

University of Essex

Yuantao Xie

University of International Business and Economics (UIBE)

Date Written: March 29, 2019

Abstract

Decision-makers who usually face model/parameter risk may prefer to act prudently by identifying optimal contracts that are robust to such sources of uncertainty. In this paper, we tackle this issue under a finite uncertainty set that contains a number of probability models that are candidates for the “true”, but unknown model. Various robust optimisation models are proposed, some of which are already known in the literature, and we show that all of them can be efficiently solved. Numerical experiments are run for various risk preference choices and it is found that for relatively large sample size, the modeler should focus on finding the best possible fit for the unknown probability model in order to achieve the most robust decision. If only small samples are available, then the modeler should consider two robust optimisation models, namely the Weighted Average Model or Weighted Worst-case Model, rather than focusing on statistical tools aiming to estimate the probability model. Amongst those two, the better choice of the robust optimisation model depends on how much interest the modeler puts on the tail risk when defining its objective function. These findings suggest that one should be very careful when robust optimal decisions are sought in the sense that the modeler should first understand the features of its objective function and the size of the available data, and then to decide whether robust optimisation or statistical inferences is the best practical approach.

Keywords: Optimal reinsurance, Risk measure, Robust optimisation, Second order conic programming, Uncertainty modelling

JEL Classification: G22

Suggested Citation

Asimit, Alexandru Vali and Hu, Junlei and Xie, Yuantao, Optimal Robust Insurance with a Finite Uncertainty Set (March 29, 2019). Available at SSRN: https://ssrn.com/abstract=3107197 or http://dx.doi.org/10.2139/ssrn.3107197

Alexandru Vali Asimit

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

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Junlei Hu

University of Essex ( email )

Wivenhoe Park
Colchester, Essex CO4 3SQ
United Kingdom

Yuantao Xie (Contact Author)

University of International Business and Economics (UIBE) ( email )

10, Huixin Dongjie
Changyang District
Beijing, Beijing 100029
China

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
67
Abstract Views
657
rank
374,544
PlumX Metrics