Survival probability in the Cramér-Lundberg model with investment is a C² classical solution to the integro-differential equation under minimal continuity and moment conditions on claims.
Viscosity solutions of the integro-differential equation for the Cram\'er--Lundberg model with annuity payments and investments
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abstract
This note is an addendum to the work initiated by Promyslov on the integro-differential equation arising in the ruin problem for annuity payment models. First, the existence of viscosity solutions is proved. Then the regularity of these solutions is established, showing that they are indeed classical solutions.
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Existence of a classical solution to the integro-differential equation arising in the Cram\'er--Lundberg non-life insurance model with proportional investment
Survival probability in the Cramér-Lundberg model with investment is a C² classical solution to the integro-differential equation under minimal continuity and moment conditions on claims.