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Regular version of the site

Article

Viscosity solutions of integro-differential equations for nonruin probabilities

Theory of Probability and Its Applications. 2016. Vol. 60. No. 4. P. 671-679.
Belkina T. A., Kabanov Y.

We consider a model of an insurance company investing its reserve into a risky asset whose price follows a geometric Lévy process. We show that the nonruin probability is a viscosity solution of a second order integro-differential equation and prove a uniqueness theorem for the latter.