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Research Article

Optimal dividend bands revisited: a gradient-based method and evolutionary algorithms

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Pages 788-810 | Received 04 Jul 2022, Accepted 10 Nov 2022, Published online: 27 Nov 2022

References

  • Albrecher H. & Thonhauser S. (2009). Optimality results for dividend problems in insurance. RACSAM-Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 103(2), 295–320.
  • Asmussen S. & Albrecher H. (2010). Ruin probabilities, Vol. 14. Singapore: World Scientific.
  • Avanzi B. (2009). Strategies for dividend distribution: A review. North American Actuarial Journal 13(2), 217–251.
  • Avram F., Palmowski Z. & Pistorius M. R. (2007). On the optimal dividend problem for a spectrally negative Lévy process. The Annals of Applied Probability 17(1), 156–180.
  • Avram F., Palmowski Z. & Pistorius M. R. (2015). On gerber–shiu functions and optimal dividend distribution for a Lévy risk process in the presence of a penalty function. The Annals of Applied Probability 25(4), 1868–1935.
  • Azcue P. & Muler N. (2005). Optimal reinsurance and dividend distribution policies in the cramér-lundberg model. Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics 15(2), 261–308.
  • Azcue P. & Muler N. (2012). Optimal dividend policies for compound poisson processes: The case of bounded dividend rates. Insurance: Mathematics and Economics 51(1), 26–42.
  • Berdel J. (2014). Optimale Bandstrategien für Dividendenzahlungen im Cramér-Lundberg-Modell [PhD thesis]. Karlsruher Instituts für Technologie.
  • Beyer H.-G. (2001). The theory of evolution strategies. Berlin, Heidelberg: Springer Science & Business Media.
  • Beyer H.-G. & Schwefel H.-P. (2002). Evolution strategies–a comprehensive introduction. Natural Computing 1(1), 3–52.
  • Gerber H. U. (1969). Entscheidungskriterien für den zusammengesetzten Poisson-Prozess [PhD thesis]. ETH Zurich.
  • Gerber H. U., Lin X. S. & Yang H. (2006). A note on the dividends-penalty identity and the optimal dividend barrier. ASTIN Bulletin 36(2), 489–503.
  • Gerber H. U. & Shiu E. S. (1998). On the time value of ruin. North American Actuarial Journal 2(1), 48–72.
  • Hubalek F. & Kyprianou E. (2011). Old and new examples of scale functions for spectrally negative Lévy processes. In Seminar on Stochastic Analysis, Random Fields and Applications VI, edited by Robert Dalang, Marco Dozzi, and Francesco Russo. Basel: Birkhäuser. P. 119–145.
  • Kramer O. (2010). A review of constraint-handling techniques for evolution strategies. Applied Computational Intelligence and Soft Computing 2010, 69–79.
  • Kuznetsov A., Kyprianou A. E. & Rivero V. (2012). The theory of scale functions for spectrally negative Lévy processes. In Lévy Matters II.Berlin, Heidelberg: Springer. P. 97–186.
  • Kyprianou A. E. (2014). Fluctuations of Lévy processes with applications: Introductory lectures. Berlin, Heidelberg: Springer Science & Business Media.
  • Lee C.-Y. & Yao X. (2004). Evolutionary programming using mutations based on the Lévy probability distribution. IEEE Transactions on Evolutionary Computation 8(1), 1–13.
  • Lin X. S., Willmot G. E. & Drekic S. (2003). The classical risk model with a constant dividend barrier: Analysis of the gerber–shiu discounted penalty function. Insurance: Mathematics and Economics 33(3), 551–566.
  • Loeffen R. L. (2008). On optimality of the barrier strategy in de finetti's dividend problem for spectrally negative Lévy processes. The Annals of Applied Probability 18, 1669–1680.
  • Román S., Villegas A. M. & Villegas J. G. (2018). An evolutionary strategy for multiobjective reinsurance optimization. Journal of the Operational Research Society 69(10), 1661–1677.
  • Rudolph G. (1996). Convergence of evolutionary algorithms in general search spaces. In Proceedings of IEEE International Conference on Evolutionary Computation, Nagoya, Japan.IEEE. P. 50–54.
  • Salcedo-Sanz S., Carro-Calvo L., Claramunt M., Castañer A. & Mármol M. (2014). Effectively tackling reinsurance problems by using evolutionary and swarm intelligence algorithms. Risks 2(2), 132–145.
  • Schmidli H. (2006). Optimisation in non-life insurance. Stochastic Models 22(4), 689–722.
  • Schmidli H. (2007). Stochastic control in insurance. London: Springer Science & Business Media.
  • Yao X., Liu Y. & Lin G. (1999). Evolutionary programming made faster. IEEE Transactions on Evolutionary Computation 3(2), 82–102.

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