Optimality of general reinsurance contracts under CTE risk measure

By formulating a constrained optimization model, we address the problem of optimal reinsurance design using the criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer’s total risk. For completeness, we analyze the optimal reinsurance model under both binding and u...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2011-09, Vol.49 (2), p.175-187
Main Authors: Tan, Ken Seng, Weng, Chengguo, Zhang, Yi
Format: Article
Language:English
Subjects:
Ceded loss function
Conditional tail expectation (CTE)
Convex analysis
Directional derivative
Economic analysis
Economic models
Economic theory
Expectation premium principle
Financial risks
Insurance premiums
Lagrangian method
Measurement
Optimal reinsurance
Optimal reinsurance Ceded loss function Conditional tail expectation (CTE) Expectation premium principle Convex analysis Lagrangian method Directional derivative Subdifferential
Optimization techniques
Reinsurance
Risk assessment
Studies
Subdifferential
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Summary:By formulating a constrained optimization model, we address the problem of optimal reinsurance design using the criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer’s total risk. For completeness, we analyze the optimal reinsurance model under both binding and unbinding reinsurance premium constraints. By resorting to the Lagrangian approach based on the concept of directional derivative, explicit and analytical optimal solutions are obtained in each case under some mild conditions. We show that pure stop-loss ceded loss function is always optimal. More interestingly, we demonstrate that ceded loss functions, that are not always non-decreasing, could be optimal. We also show that, in some cases, it is optimal to exhaust the entire reinsurance premium budget to determine the optimal reinsurance, while in other cases, it is rational to spend less than the prescribed reinsurance premium budget.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2011.03.002