An evolutionary strategy for multiobjective reinsurance optimizationFootnote

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References

• Arrow, K. J. (1974). Optimal insurance and generalized deductibles. Scandinavian Actuarial Journal, 1974(1), 1–42.
   Google Scholar
• Avanzi, B., Taylor, G., & Wong, B. (2016). Correlations between insurance lines of business: An illusion or a real phenomenon? Some methodological considerations. ASTIN Bulletin, 46(2), 225–263.
   Web of Science ®Google Scholar
• Balbás, A., Balbás, B., Balbás, R., & Heras, A. (2015). Optimal reinsurance under risk and uncertainty. Insurance: Mathematics and Economics, 60, 61–74.
   Web of Science ®Google Scholar
• Beyer, H.-G., & Schwefel, H.-P. (2002). Evolution strategies. Natural Computing, 1(1), 3–52.
   Google Scholar
• Borch, K. (1969). The optimal reinsurance treaty. Astin Bulletin, 5(2), 293–297.
   Google Scholar
• Brown, L., Beria, A. A., Carmona Cortes, O. A., Rau-Chaplin, A., Wilson, D., & Burke, N. (2014). Parallel MO-PBIL: Computing Pareto optimal frontiers efficiently with applications in reinsurance analytics. In International Conference on High Performance Computing & Simulation (HPCS) (pp. 766–775). IEEE.
   Google Scholar
• Carmona Cortes, O. A., & Rau-Chaplin, A. (2015). A modified multiobjective DE algorithm with application in reinsurance analytics. In T. Klemas & S. Chan (Eds.), Fourth International Conference on Data Analytics (pp. 51–58). IARIA.
   Google Scholar
• Carmona Cortes, O. A., Rau-Chaplin, A., & do Prado, P. F. (2014a). On VEPSO and VEDE for solving a treaty optimization problem. In F. Laux (Ed.), 2014 IEEE International Conference on Systems, Man, and Cybernetics (pp. 2427–2432). IEEE.
   Google Scholar
• Carmona Cortes, O. A., Rau-Chaplin, A., Wilson, D., & Gaiser-Porter, J. (2013). Efficient optimization of reinsurance contracts using discretized PBIL. In F. Laux (Ed.), Second International Conference on Data Analytics (pp. 18–24). IARIA.
   Google Scholar
• Carmona Cortes, O. A., Rau-Chaplin, A., Wilson, D., & Gaiser-Porter, J. (2014b). On PBIL, DE and PSO for optimization of reinsurance contracts. In A. I. Esparcia-Alcazar & A. M. Mora (Eds.), Applications of evolutionary computation, volume lecture notes in computer science 8602 (pp. 227–238). Berlin: Springer.
   Google Scholar
• Centeno, M. d. L. (2004). Retention and reinsurance programmes. In J. Teugels & B. Sundt (Eds.), Encyclopedia of actuarial science (Vol. 3, pp. 1443–1452). Wiley.
   Google Scholar
• Centeno, M. d. L., & Simões, O. (2009). Optimal reinsurance. RACSAM— Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 103(2), 387–404.
   Google Scholar
• Coello, C. C. A. (2011). Evolutionary multiobjective optimization. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 1(5), 444–447.
   Web of Science ®Google Scholar
• Deb, K. (2000). An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering, 186(2), 311–338.
   Web of Science ®Google Scholar
• Deb, K., & Agrawal, R. B. (1994). Simulated binary crossover for continuous search space. Complex Systems, 9(3), 1–15.
   Google Scholar
• Deb, K., Mohan, M., & Mishra, S. (2003). A fast multi-objective evolutionary algorithm for finding well-spread Pareto-optimal solutions. Technical Report KanGAL 2003002, lndian Institute Of Technology Kanpur.
   Google Scholar
• Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197.
   Web of Science ®Google Scholar
• Deelstra, G., & Plantin, G. (2013). Risk theory and reinsurance. EAA Series. London: Springer.
   Google Scholar
• Denuit, M., Dhaene, J., Goovaerts, M., & Kaas, R. (2006). Actuarial theory for dependent risks: Measures, orders and models. New York, NY: Wiley.
   Google Scholar
• Durillo, J. J., & Nebro, A. J. (2011). Jmetal: A java framework for multiobjective optimization. Advances in Engineering Software, 42(10), 760–771.
   Web of Science ®Google Scholar
• Ehrgott, M. (2006). Multicriteria optimization. Berlin: Springer.
   Google Scholar
• Embrechts, P., & Frei, M. (2008). Panjer recursion versus FFT for compound distributions. Mathematical Methods of Operations Research, 69(3), 497–508.
   Web of Science ®Google Scholar
• Fleischer, M. (2003). The measure of Pareto optima applications to multi-objective metaheuristics. In International Conference on Evolutionary Multi-criterion optimization (pp. 519–533). Berlin: Springer.
   Google Scholar
• Gajek, L., & Zagrodny, D. (2000). Insurer’s optimal reinsurance strategies. Insurance: Mathematics and Economics, 27(1), 105–112.
   Web of Science ®Google Scholar
• Gajek, L., & Zagrodny, D. (2004). Optimal reinsurance under general risk measures. Insurance: Mathematics and Economics, 34(2), 227–240.
   Web of Science ®Google Scholar
• Gerber, H. U. (1979). An introduction to mathematical risk theory. S.S. Huebner Foundation Monograph Series. S.S: Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania.
   Google Scholar
• Gerber, H. U. (1982). On the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums. Insurance: Mathematics and Economics, 1(1), 13–18.
   Web of Science ®Google Scholar
• Hardy, M. R. (2006). An introduction to risk measures for actuarial applications. SOA Syllabus Study Note.
   Google Scholar
• Hossack, I., Pollard, J., & Zehnwirth, B. (1999). Introductory statistics with applications in general insurance. Cambridge: Cambridge University Press.
   Google Scholar
• Jankauskas, L., & McLafferty, S. (1996). Bestfit, distribution-fitting software by palisade corporation. In Proceedings of the 28th Conference on Winter Simulation, WSC ‘96 (pp. 551–555). Washington, DC, USA: IEEE Computer Society.
   Google Scholar
• Jaszkiewicz, A. (2004). Evaluation of multiple objective metaheuristics. In X. Gandibleux, M. Sevaux, K. Sörensen, & V. T’Kindt (Eds.), Metaheuristics for multiobjective optimisation (pp. 65–89). Berlin: Springer.
   Google Scholar
• Kaluszka, M. (2001). Optimal reinsurance under mean-variance premium principles. Insurance: Mathematics and Economics, 28(1), 61–67.
   Web of Science ®Google Scholar
• Kaluszka, M. (2004). Mean variance optimal reinsurance arrangements. Scandinavian Actuarial Journal, 2004(1), 28–41.
   Google Scholar
• Knowles, J., & Corne, D. (1999). The Pareto archived evolution strategy: A new baseline algorithm for Pareto multiobjective optimisation. In Proceedings of the 1999 Congress on Evolutionary Computation (pp. 98–105). IEEE.
   Google Scholar
• Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91.
   Web of Science ®Google Scholar
• Metaxiotis, K., & Liagkouras, K. (2012). Multiobjective evolutionary algorithms for portfolio management: A comprehensive literature review. Expert Systems with Applications, 39(14), 11685–11698.
   Web of Science ®Google Scholar
• Mitschele, A., Oesterreicher, I., Schlottmann, F., & Seese, D. (2007). Heuristic optimization of reinsurance programs and implications for reinsurance. In K.-H. Waldmann & U. M. Stocker (Eds.), Operations research proceedings 2006 (pp. 287–292). Berlin: Springer.
   Google Scholar
• Oesterreicher, I., Mitschele, A., Schlottmann, F., & Seese, D. (2006). Comparison of multi-objective evolutionary algorithms in optimizing combinations of reinsurance contracts. In Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation—GECCO ‘06 (pp. 747–748).
   Google Scholar
• Ponsich, A., Jaimes, A. L., & Coello, C. C. A. (2013). A survey on multiobjective evolutionary algorithms for the solution of the portfolio optimization problem and other finance and economics applications. IEEE Transactions on Evolutionary Computation, 17(3), 321–344.
   Web of Science ®Google Scholar
• Robertson, J. P. (1992). The computation of aggregate loss distributions. Proceedings of the Casualty Actuarial Society , LXXIX(150), 57–133.
   Google Scholar
• Salcedo-Sanz, S., Carro-Calvo, L., Claramunt, M., Castaner, A., & Mármol, M. (2014). Effectively tackling reinsurance problems by using evolutionary and swarm intelligence algorithms. Risks, 2(2), 132–145.
   Google Scholar
• Scott, J. (1995). Fault tolerant design using single and multi-criteria genetic algorithms. Master’s thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology.
   Google Scholar
• Simões, O., & Centeno, M. d. L. (2008). Reinsurance. In E. L. Melnick & B. S. Everitt (Eds.), Encyclopedia of Quantitative Risk Analysis and Assessment (pp. 1425–1428). Wiley.
   Google Scholar
• Tan, K. S., & Weng, C. (2011). Enhancing insurer value using reinsurance and value-at-risk criterion. The Geneva Risk and Insurance Review, 37(1), 109–140.
   Web of Science ®Google Scholar
• Verlaak, R., & Beirlant, J. (2003). Optimal reinsurance programs. An optimal combination of several reinsurance protections on a heterogeneous insurance portfolio. Insurance: Mathematics and Economics, 33(2), 381–403.
   Web of Science ®Google Scholar
• Vilar, J. L. (2000). Arithmetization of distributions and linear goal programming. Insurance: Mathematics and Economics, 27(1), 113–122.
   Web of Science ®Google Scholar
• Zitzler, E., & Thiele, L. (1998). Multiobjective optimization using evolutionary algorithms—A comparative case study. In International Conference on Parallel Problem Solving from Nature (pp. 292–301). Berlin: Springer.
   Google Scholar