Establishes that ruin probability Ψ(u) decays exactly as C* u^{-β} for large u in the Sparre Andersen model with Lévy investments, where β is the Cramér root.
Exact solution of the ruin problem in the Cram\'er--Lundberg model with proportional investment
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abstract
The Cram\'er-Lundberg model with exponential claims and proportional investment is solved exactly: the integro-differential equation for the survival probability reduces to a doubly confluent Heun equation, yielding an explicit solution in terms of Heun functions, a verification theorem, and a qualitative analysis of ruin probability versus investment share.
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2026 1verdicts
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Exact asymptotics of the ruin probability in the Sparre Andersen model
Establishes that ruin probability Ψ(u) decays exactly as C* u^{-β} for large u in the Sparre Andersen model with Lévy investments, where β is the Cramér root.