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On finite-time ruin probabilities for general risk models. (English) Zbl 1300.91037

Summary: We proved the formula calculating the ruin probability for a general risk model. We generalized the Picard-Lefèvre formula (see [P. Picard and C. Lefèvre, Scand. Actuar. J. 1997, No. 1, 58–69 (1997; Zbl 0926.62103)]) for ruin probability of compound binomial risk model as well as the results of C. Lefèvre and L. Stéphane [ibid. 2008, No. 1, 41–60 (2008; Zbl 1164.91033)]. In their studies, the authors gave the formula of ruin probability for classical risk model only while in our study, we figured out the formula for a general risk model.

MSC:

91B30 Risk theory, insurance (MSC2010)
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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