Ruin probabilities with investments in random environment: smoothness

2023/11/18 by Antipov, Viktor, Kabanov, Yuri · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2311.11023

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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• On the Application of Laplace Transform to the Ruin Problem with Random Insurance Payments and Investments in a Risky Asset

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