Existence of viscosity solutions is proved for the integro-differential ruin equation in the annuity-and-investment Cramér-Lundberg model, followed by a regularity result establishing that the solutions are classical.
North-Holland, Amsterdam (1981) Viscosity solutions for the Cram´ er–Lundberg model 13
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Viscosity solutions of the integro-differential equation for the Cram\'er--Lundberg model with annuity payments and investments
Existence of viscosity solutions is proved for the integro-differential ruin equation in the annuity-and-investment Cramér-Lundberg model, followed by a regularity result establishing that the solutions are classical.