Power tailed ruin probabilities in the presence of risky investments.
The paper derives two-sided bounds for the ruin probability of an insurance business that invests reserves in assets with Lévy process-driven returns. The claims less premiums cash flow is also Lévy with no common jumps with the returns. Then the reserve process of the insurance company itself belongs to the Lévy class. Special cases would include combinations of Brownian and Poisson processes for claims and returns as well as return processes with infinitely many jumps in every finite period in conjunction with Brownian claims. It is shown that the probability of ruin as a function of initial reserve level has a power function lower bound, provided that returns can get negative and losses are big enough. If the discretized compound return process satisfies an analogue of the Cramér condition, an upper ruin probability bound in a power function form exists as well. A more strong asymptotic property for the ruin probability in a power function form is obtained when discretized compound returns have a non-lattice distribution.
scientific article; zbMATH DE number 2138954