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arXiv · 2401.04276

Ruin problems with investments on a finite interval: PIDEs and their viscosity solutions

Viktor Antipov·Yuri Kabanov
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Abstract

The study deals with the ruin problem when an insurance company invests its reserve in a risky asset whose the price dynamics is given by a geometric L\'evy process. Considering the ruin probability as a of the capital reserve we obtain for it a partial integro-differential equation understood in a viscosity sense and prove a result on the uniqueness of the viscosity solution for a corresponding boundary value problem.

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Viktor Antipov, Yuri Kabanov. 2024-01-08. Ruin problems with investments on a finite interval: PIDEs and their viscosity solutions. https://arxiv.org/abs/2401.04276

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