On tail probabilities and first passage times for fractional Brownian motion

Zbigniew Michna

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,

ISSN 0281-1944

In the paper we present a method of simulation of ruin probability over infinite horizon for fractional Brownian motion with parameter of self-similarity H > ½. We derive some theoretical results which show how fast the method works. As an application of our method we compute the Picands constant for fractional Brownian motion.
Key words:
fractional Brownian motion, simulation of ruin probability, Monte Carlo method, Picands constant