Ruin probabilities for a Lévy-driven generalised Ornstein-Uhlenbeck process A. M. Kabanov, S. M. Pergamenshchikov
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ArticleContent type: Текст Media type: электронный Subject(s): Орнштейна-Уленбека-Леви процесс | авторегрессия со случайными коэффициентами | теория обновленияGenre/Form: статьи в журналах Online resources: Click here to access online
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Finance and stochastics Vol. 24, № 1. P. 39-69Abstract: We study the asymptotic of the ruin probability for a process which is the solution of linear SDE defined by a pair of independent Levy 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 V1. We show that the ruin probability admits the exact asymptotic Cu−β as the initial capital u → ∞ assuming only that the law of VT is non-arithmetic without any further assumptions on the price process.
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We study the asymptotic of the ruin probability for a process which is the solution of linear SDE defined by a pair of independent Levy 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 V1. We show that the ruin probability admits the exact asymptotic Cu−β as the initial capital u → ∞ assuming only that the law of VT is non-arithmetic without any further assumptions on the price process.
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