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Explicit finite-time and infinite-time ruin probabilities in the continuous case. (English) Zbl 0963.91062

Summary: In this rather self-contained paper we indicate general explicit analytic expressions for finite-time and infinite-time ruin probabilities in the classical risk model corresponding to initial risk reserves \(u\geq 0\). We assume that the claimsize distribution has a density on \([0, \infty)\). Our solutions are continuous versions of discrete expressions by Picard and Lefèvre but our methodology is different and the continuous formulas have a component with no counterpart in the discrete case [cf. P. Picard and C. Lefèvre, The probability of ruin in finite time with discrete claim size distribution. Scan. Actuar. J. 1, 58-69 (1997)].

MSC:

91B30 Risk theory, insurance (MSC2010)
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References:

[1] De Vylder, F., 1996. Advanced Risk Theory. A Self-Contained Introduction. Presses de l’Université de Bruxelles & Swiss Association of actuaries.; De Vylder, F., 1996. Advanced Risk Theory. A Self-Contained Introduction. Presses de l’Université de Bruxelles & Swiss Association of actuaries.
[2] De Vylder F., 1998. Numerical finite-time ruin probabilities by the Picard-Lefèvre formula, Scandinavian Actuarial Journal, to be published.; De Vylder F., 1998. Numerical finite-time ruin probabilities by the Picard-Lefèvre formula, Scandinavian Actuarial Journal, to be published.
[3] 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
[4] Wikstad, N., 1971. Exemplification of ruin probabilities. The ASTIN Bulletin VI (2), 147-152.; Wikstad, N., 1971. Exemplification of ruin probabilities. The ASTIN Bulletin VI (2), 147-152.
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