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This note is a complement to the paper by Eberlein, Kabanov, and Schmidt onthe asymptotic of the ruin probability in a Sparre Andersen non-life insurancemodel with investments a risky asset whose price follows a geometric L\'evyprocess. Using the techniques of semi-Markov processes we extend the result ofthe mentioned paper to the case of annuities and models with two-sided jumps.

Ruin Probabilities for a Sparre Andersen Model with Investments: the Case of Annuity Payments