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An improved finite-time ruin probability formula and its $$Mathematica$$ implementation. (English) Zbl 1074.62528
Summary: An improved version of a ruin probability formula due to Z.G. Ignatov and V.K. Kaishev [Scand. Actuarial J. 2000, No. 1, 46–62 (2000; Zbl 0958.91030)], allowing for the exact evaluation of the finite-time survival probability for discrete, dependent, individual claims, Poisson claim arrivals and arbitrary, increasing premium income function is derived. Its numerical efficiency is studied, using the Mathematica system. Numerical results are provided and computational aspects are discussed. A Mathematica module, realizing the P. Picard and C. Lefèvre [ibid. 1997, No. 1, 58–69 (1997; Zbl 0926.62103)] formula has also been developed and used for numerical investigations.
Reviewer: Reviewer (Berlin)

##### MSC:
 62P05 Applications of statistics to actuarial sciences and financial mathematics 65C60 Computational problems in statistics (MSC2010)
Mathematica
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##### References:
 [1] Dickson, D.C.M., 1999. On numerical evaluation of finite time survival probabilities. British Actuarial Journal 5 (III), 575-584. [2] De Vylder, F.E., La formule de Picard et lefèvre pour la probabilite de ruine en temps fini, Bulletin français d’actuariat, 1, 2, 31-40, (1997) [3] De Vylder, F.E., Numerical finite-time ruin probabilities by the picard – lefèvre formula, Scandinavian actuarial journal, 2, 97-105, (1999) · Zbl 0952.91042 [4] Ignatov, Z.G.; Kaishev, V.K., Two-sided bounds for the finite time probability of ruin, Scandinavian actuarial journal, 1, 46-62, (2000) · Zbl 0958.91030 [5] Ignatov, Z.G., Kaishev, V.K., Krachunov, R.S., 2000. Explicit, finite time ruin probabilities for discrete, dependent claims. Technical Report No. 3. Section on Comp. Stochastics, Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria. [6] Kaishev, V.K., Krachunov, R.S., 2000. A Mathematica package for calculating finite time ruin probabilities in the case of discrete claim size distributions. Technical Report No. 1. Section on Comp. Stochastics, Institute of Mathematics, Bulgarian Academy of Sciences, Mathematica Journal, in preparation. [7] Picard, P.; Lefèvre, C., The probability of ruin in finite time with discrete claim size distribution, Scandinavian actuarial journal, 1, 58-69, (1997) · Zbl 0926.62103
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