Abstract
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 Lévy 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 (uto infty ), assuming only that the law of (V_{T}) is non-arithmetic without any further assumptions on the price process.