Dynamic Importance Sampling for Heavy-Tailed Random Walks

Specialeforsvar: Jørgen Carøe

Titel: Dynamic Importance Sampling for Heavy-Tailed Random Walks

Resume: The aim of this thesis is to examine and develop a method for estimating probabilities of ultimate ruin in the case of random walks with heavy-tailed increments. To this end, we introduce the notion of dynamic importance sampling, where the importance sampling distribution is state-dependent. For light-tailed distributions we will present a dynamic importance sampling estimator based on exponential twisting. This has favourable properties, but cannot be used for the heavy-tailed situation. We use Markov chain theory to develop an importance sampling method which does not make use of exponential twisting, but show that it possesses similar properties, including bounded relative error. We conclude the paper with a numerical study and a discussion of the method.

Vejleder: Jeffrey F. Collamore
Censor: Anders Hedegaard Jessen