The survival probability in the Cramér-Lundberg model with exponential claims and proportional investment is expressed explicitly using Heun functions after the governing integro-differential equation reduces to a doubly confluent Heun equation.
Existence of a classical solution to the integro-differential equation arising in the Cram\'er--Lundberg non-life insurance model with proportional investment
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abstract
This paper establishes that the survival probability in the non-life Cram\'{e}r--Lundberg insurance model with proportional investment is a classical $C^2$-solution of the associated integro-differential equation under minimal moment conditions: it suffices that the claim size distribution is continuous and possesses a finite moment of some positive order.
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Exact solution of the ruin problem in the Cram\'er--Lundberg model with proportional investment
The survival probability in the Cramér-Lundberg model with exponential claims and proportional investment is expressed explicitly using Heun functions after the governing integro-differential equation reduces to a doubly confluent Heun equation.