SECOND ORDER CONE PROGRAMMING APPROACH FOR OPTIMAL REINSURANCE

In this study, we propose an optimal retention for practical reinsurance problems via conditional tail expectation and variance-minization models. We add an additional constraint, which expresses solvency of an insurance company, to the reinsurance optimization problems based on classical premium principles, namely expectation premium and standard deviation premium principle. Moreover, optimal solution of the reinsurance optimization problems in real claim data is solved by reformulating into equivalent second-order cone programming problems. We use CVXR package of R programming to solve the equivalent problems. Finally, we make some recommendations to apply in practice.