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Theoretical and empirical study on optimal insurance and reinsurance design

Hu, J. (2018). Theoretical and empirical study on optimal insurance and reinsurance design. (Unpublished Doctoral thesis, City, University of London)

Abstract

Insurance and reinsurance are important tools of risk management. A well-designed (re)insurance strategy can help individuals and institutions to effectively adjust its risk position to match its risk appetite while meeting other targets such as profitability. Thus, optimal (re)insurance design has been a popular research area during the last fifty years.

The first contribution investigates the optimal reinsurance contract from the perspective of an insurer who would like to minimise its risk exposure under Solvency II. Under this regulatory framework, the insurer is exposed to the retained risk, reinsurance premium and change in the risk margin requirement as a result of reinsurance. Depending on how the risk margin corresponding to the reserve risk is calculated, two optimal reinsurance problems are formulated. We show that the optimal reinsurance policy can be in the form of two layers. Further, numerical examples illustrate that the optimal two-layer reinsurance contracts are only slightly different under these two methodologies.

In the second contribution, numerical optimisation methods that are practically implementable and solvable are discussed with actuarial applications. 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 effciency across the entire organisation.

The next two contributions aim to identify a robust optimal insurance contract that is not sensitive to the chosen risk distribution. The first of the two contributions focuses on the classical robust optimisation models, namely the worst-case and the worst-regret model, which have been already investigated in literature relating to optimal investment portfolio problems, while Bayesian type robust optimisation models are discussed in the second contribution. A caveat of robust optimisation is that the optimal solution may not be unique, and therefore, it may not be economically acceptable, i.e. not Pareto optimal. This issue is numerically addressed and simple numerical methods are found for constructing insurance contracts that are both Pareto and robust optimal.

Publication Type: Thesis (Doctoral)
Subjects: H Social Sciences > HG Finance
Departments: Cass Business School > Actuarial Science & Insurance
Doctoral Theses
Doctoral Theses > Cass
URI: http://openaccess.city.ac.uk/id/eprint/20566
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