<Para ID="Par1">We obtain an explicit expression for the price of a vulnerable claim written on a stock whose predefault dynamics follows a Lévy-driven SDE. The stock jumps to zero at default with a hazard rate given by a negative power of the stock price. We recover the characteristic function of the terminal...</para>

In this article the forward rates equation of the Musiela model is analysed. The equation is studied in the Sobolev spaces $H^1_\gamma({\Bbb R}^+)$ and $H^1({\Bbb R}^+)$. Explicit mild solutions and equivalent conditions for the existence and uniqueness of invariant measures are presented.

In this paper we analyse a stochastic volatility model that is an extension of the traditional Black-Scholes one. We price European options on several assets by using a superstrategy approach. We characterize the Markov superstrategies, and show that they are linked to a nonlinear PDE, called...