This paper addresses the estimation of default probabilities and associated confidence sets with special focus on rare events. Research on rating transition data has documented a tendency for recently downgraded issuers to be at an increased risk of experiencing further downgrades compared to...

A new kind of drift function based on the Laplace transform of rotation symmetric measures on is introduced and applied to the class of the so-called affine Markov chains. An example is given where this approach provides a better criterion for geometric drift than standard drift functions.

In this paper we derive conditions for geometric ergodicity of the random-walk-based Metropolis algorithm on . We show that at least exponentially light tails of the target density is a necessity. This extends the one-dimensional result of Mengersen and Tweedie (1996, Ann. Statist. 24, 101-121)....