The ruin problem for Lévy-driven linear stochastic equations with applications to actuarial models with negative risk sums

2016/04/21 by Yuri Kabanov, Serguei Pergamenchtchikov, Kabanov, Yuri +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1604.06370

openalex publication_date 2016/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic of the ruin probability for a process which is the solution of linear SDE defined by a pair of independent Lévy processes. Our main interest is the model describing the evolution of the capital reserve of an insurance company selling annuities and investing in a risky asset. Let β>0 be the root of the cumulant-generating function H of the increment of the log price process V. We show that the ruin probability admits the exact asymptotic Cu^-β as the initial capital u→∞ assuming only that the law of V_T is non-arithmetic without any further assumptions on the price process.

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