Ruin probabilities for a Lévy-driven generalized Ornstein-Uhlenbeck process

International audienceWe 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 1. 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