Ruin probabilities for a Levy-driven generalised Ornstein-Uhlenbeck process

We study the asymptotics of the ruin probability for a process which is the solution of a linear SDE defined by a pair of independent Levy processes. Our main interest is a model describing the evolution of the capital reserve of an insurance company selling annuities and investing in a risky asset. Let beta > 0 be the root of the cumulant-generating function H of the increment V-1 of the log-price process. We show that the ruin probability admits the exact asymptotic Cu-beta as the initial capital u -> infinity, assuming only that the law of V-T is non-arithmetic without any further assumptions on the price process.