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The maximum surplus distribution before ruin in an Erlang(\(n\)) risk process perturbed by diffusion. (English) Zbl 1237.91145

Summary: We consider the distribution of the maximum surplus before ruin in a generalized Erlang(\(n)\) risk process (i.e., convolution of \(n\) exponential distributions with possibly different parameters) perturbed by diffusion. It is shown that the maximum surplus distribution before ruin satisfies the integro-differential equation with certain boundary conditions. Explicit expressions are obtained when claims amounts are rationally distributed. Finally, the surplus distribution at the time of ruin and the surplus distribution immediately before ruin are presented.

MSC:

91B30 Risk theory, insurance (MSC2010)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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