ИСТИНА

In the classical collective risk theory it is usually assumed that the capital reserve of a company is placed in a bank account paying zero interest. In the recent three decades the theory was extended to cover a more realistic situation where the reserve is invested, fully or partially, in a risky asset (e.g., in a portfolio evolving as a market index). This natural generalization generates a huge variety of new ruin problems which can be considered as the exit problem for a semimartingale Ornstein-Uhlenbeck process. Roughly speaking, each “classical” ruin problem, e.g., a version of the Cramer-Lundberg model (for the non-life insurance, for the annuity payments etc.) can be combined with a model of price of the risky security (geometric Brownian motion, geometric Lévy process, various models with stochastic volatilities, etc.). In the talk we present new asymptotic results for the ruin probabilities, in particular, for the Sparre Andersen type models with risky investments having the geometric Lévy dynamics and for Cramér-Lundberg type models with investments in a risky asset with a regime switching price.