Ruin Probabilities with Investments in Random Environment: Smoothness

Viktor Antipov and Yuri Kabanov ()
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Viktor Antipov: Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow 119234, Russia
Yuri Kabanov: Moscow School of Economics, Lomonosov Moscow State University, Moscow 119234, Russia

Mathematics, 2024, vol. 12, issue 11, 1-12

Abstract: This 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 random variations in the economic and financial environments. We prove a sufficient condition on the distribution of jumps of the business process ensuring the smoothness of the ruin probability as a function of the initial capital and obtain for this function an integro-differential equation.

Keywords: ruin probabilities; actuarial models with investments; smoothness of ruin probabilities; stochastic volatility; regime switching; integro-differential equations for ruin probabilities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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