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Risk theory with a nonlinear dividend barrier. (English) Zbl 1076.91521
Summary: In the framework of classical risk theory we investigate a surplus process in the presence of a nonlinear dividend barrier and derive equations for two characteristics of such a process, the probability of survival and the expected sum of discounted dividend payments. Number-theoretic solution techniques are developed for approximating these quantities and numerical illustrations are given for exponential claim sizes and a parabolic dividend barrier.

MSC:
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
65C05 Monte Carlo methods
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