Viscosity solutions of the integro-differential equation for the Cram\'er--Lundberg model with annuity payments and investments
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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