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Methods to estimate the optimal dividend barrier and the probability of ruin
Insurance: Mathematics and Economics
In applications of collective risk theory, complete information about the individual claim amount distribution is often not known, but reliable estimates of its first few moments may be available. For such a situation, this paper develops methods to estimate the optimal dividend barrier and the probability of ruin. In particular, two De Vylder approximations are explained, and the first and second order diffusion approximations are examined. For several claim amount distributions, the approximate values are compared numerically with the exact values. The De Vylder and diffusion approximations can be adapted to the more general situation where the aggregate claims process is a Lévy process with nonnegative increments.
Optimal dividend barrier, ruin probability, Lévy processes, subordinators, De Vylder approximations, diffusion approximations, Lundberg function, Lundberg?s fundamental equation, gamma processes
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