Ruin probabilities with investments in a risky asset with the price given by a geometric Lévy process
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. We show that the ruin probability admits the exact asymptotic as the initial capital tends to infinity. It is given by the strictly positive root of the cumulant-generating function of the increment of log price process assuming only that such a root does exist.
Yuri Kabanov , Besançon