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Bounded Data-Driven Actuarial Maps and CVaR-Based Reinsurance Selection
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Abstract
Classical actuarial modelling usually begins with a fully specified stochastic model for mortality, claims, discount factors, assets, or aggregate losses. This article develops a complementary distribution-light approach in which the actuarial object of interest is fitted directly from data or scenarios. Sigmoidal parametrisations are useful in this setting because they give stable bounded maps and, when placed behind suitable links or constraints, can produce probability-valued, positive, or monotone actuarial functionals. The paper first records admissible sigmoidal architectures for survival probabilities, reserves, ruin probabilities, and risk measures, and states basic guarantees on boundedness, Lipschitz stability, existence of empirical minimisers, and consistency. The main applied component is a finite quoted reinsurance menu: given scenario losses and stop-loss premiums quoted by a reinsurer, the insurer selects the retention that minimises reinsurance premium plus empirical CVaR of the retained loss. The option analogy is made precise: stop-loss indemnity is a call payoff on the loss variable; the insurer is long this indemnity layer, while the reinsurer is short the layer in exchange for premium. Thus reinsurance operates as a static tail hedge for the insurer's underwriting result.
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Bounded Data-Driven Actuarial Maps and CVaR-Based Reinsurance Selection. (2026). International Journal of Engineering, Science and Environment (IJESE), 1(1). https://ijese.in/journal/article/view/55
References
[1] P. Artzner, F. Delbaen, J.-M. Eber, and D. Heath, “Coherent measures of risk,” Mathematical Finance, vol. 9, no. 3, pp. 203–228, 1999.
[2] S. Asmussen and H. Albrecher, Ruin Probabilities, 2nd ed. Singapore: World Scientific, 2010.
[3] J. D. Cummins and P. Trainar, "Securitization, insurance, and reinsurance," Journal of Risk and Insurance, vol. 76, no. 3, pp. 463–492, 2009.
[4] G. Cybenko, “Approximation by superpositions of a sigmoidal function,” Mathematics of Control, Signals and Systems, vol. 2, no. 4, pp. 303–314, 1989.
[5] N. A. Doherty, Integrated Risk Management for Financial Firms. Upper Saddle River, NJ, USA: Prentice Hall, 2000.
[6] H. U. Gerber and E. S. W. Shiu, “On the time value of ruin,” North American Actuarial Journal, vol. 2, no. 1, pp. 48–72, 1998.
[7] J. C. Hull, Options, Futures, and Other Derivatives, 10th ed. Pearson, 2018.
[8] K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks, vol. 2, no. 5, pp. 359–366, 1989.
[9] R. Kaas, M. Goovaerts, J. Dhaene, and M. Denuit, Modern Actuarial Risk Theory: Using R, 2nd ed. Berlin, Germany: Springer, 2008.
[10] M. Leshno, V. Y. Lin, A. Pinkus, and S. Schocken, “Multilayer feedforward networks with a nonpolynomial activation function can approximate any function,” Neural Networks, vol. 6, no. 6, pp. 861–867, 1993.
[11] A. J. McNeil, R. Frey, and P. Embrechts, Quantitative Risk Management: Concepts, Techniques and Tools, 2nd ed. Princeton, NJ, USA: Princeton University Press, 2015.
[12] P. McCullagh and J. A. Nelder, Generalized Linear Models, 2nd ed. London, U.K.: Chapman and Hall, 1989.
[13] W. K. Newey and D. McFadden, “Large sample estimation and hypothesis testing,” in Handbook of Econometrics, vol. 4, R. F. Engle and D. L. McFadden, Eds. Amsterdam, The Netherlands: Elsevier, 1994, pp. 2111–2245.
[14] H. H. Panjer and G. E. Willmot, Insurance Risk Models. Schaumburg, IL, USA: Society of Actuaries, 1992.
[15] R. T. Rockafellar and S. Uryasev, “Optimization of conditional value-at-risk,” Journal of Risk, vol. 2, no. 3, pp. 21–41, 2000.
[16] R. T. Rockafellar and S. Uryasev, “Conditional value-at-risk for general loss distributions,” Journal of Banking & Finance, vol. 26, no. 7, pp. 1443–1471, 2002.