Penalisation involving the one-sided supremum for a stable Lévy process with index α∈(0, 2] is studied. We introduce the analogue of Azéma–Yor martingales for a stable Lévy process and give the law of the overall supremum under the penalised measure.
Dans cet article, nous pénalisons la loi d’une araignée brownienne prenant ses valeurs dans un ensemble fini de demi-droites concourantes, avec un poids égal à , où est un réel positif, une famille de réels indexés par , un paramètre réel, la distance de à l’origine, () la demi-droite sur laquelle se trouve , le temps local de à l’origine, et la constante de normalisation. Nous montrons que la famille des mesures de probabilité obtenue par ces pénalisations converge vers...
As in preceding papers in which we studied the limits of penalized 1-dimensional Wiener measures with certain functionals Γt, we obtain here the existence of the limit, as t → ∞, of d-dimensional Wiener measures penalized by a function of the maximum up to time t of the Brownian winding process (for d = 2), or in {d}≥ 2 dimensions for Brownian motion prevented to exit a cone before time t. Various extensions of these multidimensional penalisations are studied, and the limit laws are described....
We show how to use the Gaussian HJM model to price modified forward-start options. Using data from the Polish market we calibrate the model and price this exotic option on the term structure. The specific problems of Central Eastern European emerging markets do not permit the use of the popular lognormal models of forward LIBOR or swap rates. We show how to overcome this difficulty.
We show how to use the Gaussian HJM model to price Polish three-year bonds. %A bond issued by A Polish Treasury bond is treated as a risk-free security.