Geodesic
Approximate formulas for calculation of the optimal level of deductible
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2017), pp. 61-72 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper we considered a problem of definition of the optimal level of deductible in the case of excess-of-loss insurance. Theorem 1 concerns the case when the function of excess-of-loss insurance does not depend on the type of utility function. Theorem 3 concerns the case when the insurance premium depends on the level of deductible. For each case we defined approximate formulas for calculation of the optimal level of deductible (theorems 2, 4, and 5).
Keywords: deductible, insurance premium, actuarial value, loading factor, deterministic equivalent, exponential utility function, exponential distribution. 
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R. A. Korolev; L. K. Karamova. Approximate formulas for calculation of the optimal level of deductible. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2017), pp. 61-72. http://geodesic.mathdoc.fr/item/VTPMK_2017_3_a4/

[1] Arrow K. J., “Uncertainty and the welfare economics of medical care”, American Economic Review, 53:5 (1963), 941-973

[2] Arrow K. J., “Optimal insurance and generalized deductibles”, Collected Papers of Kenneth J., v. 3, Individual Choice under Certainty and Uncertainty, Belknap Press, Cambridge, Massachusetts, 1984, 212-260

[3] Bowers N. L., Gerber H. U., Hickman J. C., Jones D. A., Nesbitt C. J., Actuarial Mathematics, The Society of Actuaries, Itasca, Illinois, 1997, 753 pp. | MR

[4] Schlesinger H., “The optimal level of deductibility in insurance contracts”, The Journal of Risk and Insurance, 48:3 (1981), 465-481 | DOI

[5] Zorich V. A., Mathematical Analysis I, Springer-Verlag, Berlin, Heidelberg, 2015, 616 pp. | Zbl

[6] Korolev V. Yu., Bening V. E., Shorgin S. Ya., Mathematical Foundations of Risk Theory, Fizmatlit Publ., Moscow, 2011, 620 pp. (in Russian)