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Ruin problems and dual events. (English) Zbl 0803.62091
Summary: The first author [ibid. 11, 191-207 (1992; Zbl 0770.62090)] used dual events to explain results relating to the distribution of the surplus immediately prior to ruin in the classical surplus process. In this paper the authors show that dual events can be used to explain other results in ruin theory. In particular they prove and explain the relationship between the density of the surplus immediately prior to ruin, and the joint density of the surplus immediately prior to ruin and the severity of ruin.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
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[1] Bowers, N.L.; Gerber, H.U.; Hickman, J.C.; Jones, D.A.; Nesbitt, C.J., Actuarial mathematics, (1987), Society of Actuaries Itasca, IL
[2] Dickson, D.C.M.; Gray, J.R., Approximations to ruin probability in the presence of an upper absorbing barrier, Scandinavian actuarial journal, 105-115, (1984) · Zbl 0584.62174
[3] Dickson, D.C.M., On the distribution of the surplus prior to ruin, Insurance: mathematics and economics, 11, 191-207, (1992) · Zbl 0770.62090
[4] Dufresne, F.; Gerber, H.U., The surpluses immediately before and at ruin, and the amount of the claim causing ruin, Insurance: mathematics and economics, 7, 193-199, (1988) · Zbl 0674.62072
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