ИСТИНА

We study a model of an insurance company where the business activity is described by the Sparre Andersen model, that is, by a compound renewal process, while the price of the risky asset follows an independent Lévy process. The asymptotic of ruin probabilities for such models were studied in the case of upward jumps of the business process by Eberlein, Kabanov, and Schmidt and the non-life insurance version (downward jumps) and a mixture of both were treated by Kabanov and Promyslov. We discuss the looking simple case where the price process is of bounded variation with only positive or only negative jumps. Surprisingly, it happens to be rather delicate. We provide new sufficient conditions to ensure the asymptotic behavior of the ruin probability as was discovered in the previous works. Our results are based on the theory of distributional equations as presented in the book by Buraczewski, Damek, and Mikosch. Based on joint works with and Danil Legenkiy and Platon Promyslov.