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arXiv · 2311.11023

Ruin probabilities with investments in random environment: smoothness

Viktor Antipov·Yuri Kabanov
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Abstract

The paper deals with the ruin problem of an insurance company investing its capital reserve in a risky asset with the price dynamics given by a conditional geometric Brownian motion whose parameters depend on a Markov process describing a random variations in the economic and financial environments. We prove smoothness of the ruin probability as a function of the initial capital and obtain for it an integro-differential equation.

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Viktor Antipov, Yuri Kabanov. 2023-11-18. Ruin probabilities with investments in random environment: smoothness. https://arxiv.org/abs/2311.11023

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