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Ruin probabilities in the compound binomial model. (English) Zbl 0778.62099
Summary: Explicit formulas are derived for finite time ruin probabilities in the discrete time and state-space compound binomial model using the technique of generating functions. Ultimate ruin probabilities are then obtained, and a close connection is established with the ultimate ruin probabilities in the usual compound Poisson model when the claim severity distribution is a (truncated) mixed Poisson distribution.

62P05 Applications of statistics to actuarial sciences and financial mathematics
Full Text: DOI
[1] Bowers, N.; Gerber, H.; Hickman, J.; Jones, D.; Nesbitt, C., Actuarial mathematics, (1986), Society of Actuaries Itasca, IL · Zbl 0634.62107
[2] Chan, B., Ruin probability for translated combination of exponential claims., ASTIN bullletin 20, 113-114, (1986)
[3] Dufresne, F., Distributions stationnaires d’un système bonus-malus et probabilitè de ruine, ASTIN bullletin 18, 31-36, (1986)
[4] Feller, W., An introduction to probability theory and its applications, Vol. 1, (1968), Wiley New York · Zbl 0155.23101
[5] Feller, W., An introduction to probability theory and its applications, Vol. 2, (1968), Wiley New York · Zbl 0155.23101
[6] Gerber, H., An introduction to mathematical risk theory, (1979), S.S. Huebner Foundation, University of Pennyslyvania Philadelphia, PA · Zbl 0431.62066
[7] Gerber, H., Mathematical fun with the compound binomial process., ASTIN bullletin 18, 161-168, (1986)
[8] Michel, R., Representation of a time-discrete probability of eventual ruin., Insurance: mathematics and economics 8, 149-152, (1989) · Zbl 0676.62085
[9] Panjer, H., Recursive evaluation of a family of compound distributions., ASTIN bullletin 12, 22-26, (1986)
[10] Panjer, H.; Willmot, G., Insurance risk models., (1992), Society of Actuaries Schaumburg
[11] Riordan, J., An introduction to combinatorial analysis., (1958), Wiley New York · Zbl 0078.00805
[12] Shiu, E., The probability of eventual ruin in the compound binomial model., ASTIN bullletin 19, 179-190, (1989)
[13] Tijms, H., Stochastic modelling and analysis:A computational approach., (1986), Wiley Chichester
[14] Whittaker, E.; Watson, G., A course of modern analysis., (1927), Cambridge University Press London · JFM 53.0180.04
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