This paper proposes a paradigm shift in the valuation of long term contracts, away from classical no-arbitrage pricing towards pricing under the real world probability measure. In contrast to risk neutral pricing, which is a form of relative pricing, the long term average excess return of the...

The objective of this paper is to consider defaultable term structure models in a general setting beyond standard risk-neutral models. Using as numeraire the growth optimal portfolio, defaultable interest rate derivatives are priced under the real-world probability measure. Therefore, the...

This paper uses Lie symmetry group methods to obtain transition probability densities for scalar diffusions, where the diffusion coefficient is given by a power law. We will show that if the drift of the diffusion satisfies a certain family of Riccati equations, then it is possible to compute a...

This paper studies the application of exact simulation methods for multi-dimensional multiplicative noise stochastic differential equations to filtering. Stochastic differential equations with multiplicative noise naturally occur as Zakai equation in hidden Markov chain filtering. The paper...