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Keywords:

Social Sciences, Science & Technology, Physical Sciences, Economics, Mathematics, Interdisciplinary Applications, Social Sciences, Mathematical Methods, Statistics & Probability, Business & Economics, Mathematics, Mathematical Methods In Social Sciences, 01 Mathematical Sciences, 14 Economics, 15 Commerce, Management, Tourism and Services, 35 Commerce, management, tourism and services, 38 Economics, 49 Mathematical sciences

Abstract:

We derive upper and lower bounds for the ruin probability over infinite time in the classical actuarial risk model (usual independence and equidistribution assumptions; the claim-number process is Poisson). Our starting point is the renewal equation for the ruin probability, but no renewal theory is used, except for the elementary facts proved in the note. Some bounds allow a very simple new proof of an asymptotic result akin to heavy-tailed claim-size distributions. © 1984.