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Optimal Risk Transfer: A Numerical Optimisation Approach

29 Pages Posted: 20 Jun 2016 Last revised: 28 Oct 2017

Alexandru Vali Asimit

City University London - Sir John Cass Business School

Tao Gao

University of Bath - School of Mathematical Sciences; University College London

Junlei Hu

City University London - Cass Business School

Eun-Seok Kim

Middlesex University

Date Written: October 8, 2017

Abstract

Capital efficiency and asset/liability management are part of the Enterprise Risk Management Process of any insurance/reinsurance conglomerate and serve as quantitative methods to fulfill the strategic planning within an insurance organisation. There has been a considerable amount of work in this ample research field, but invariably one of the last questions is whether or not, numerically, the method is practically implementable, which is our main interest. The numerical issues are dependent upon the traits of the optimisation problem and therefore, we plan to focus on the optimal reinsurance design, which has been a very dynamic topic in the last decade. The existing literature is focused on finding closed-form solutions that are usually possible when economic, solvency, etc constraints are not included in the model. Including these constraints, the optimal contract can only be found numerically. The efficiency of these methods is extremely good for some well-behaved convex problems, such as the Second-Order Conic Problems. Specific numerical solutions are provided in order to better explain the advantages of appropriate numerical optimisation methods chosen to solve various risk transfer problems. The stability issues are also investigated together with a case study performed for an insurance group that aims capital efficiency across the entire organisation.

Keywords: Linear Programming, Optimal Reinsurance/Risk Transfer, Risk Measure, Second-Order Conic Programming

JEL Classification: C61, G22

Suggested Citation

Asimit, Alexandru Vali and Gao, Tao and Hu, Junlei and Kim, Eun-Seok, Optimal Risk Transfer: A Numerical Optimisation Approach (October 8, 2017). Available at SSRN: https://ssrn.com/abstract=2797562

Alexandru Asimit (Contact Author)

City University London - Sir John Cass Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Tao Gao

University of Bath - School of Mathematical Sciences ( email )

Bath, BA2 7AY
United Kingdom

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

Junlei Hu

City University London - Cass Business School ( email )

106 Bunhill Row
London, EC1Y8TZ
United Kingdom

Eun-Seok Kim

Middlesex University ( email )

The Burroughs
London, NW4 4BT
United Kingdom

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