In Gapeev and Kühn (2005) [8], the Dynkin game corresponding to perpetual convertible bonds was considered, when driven by a Brownian motion and a compound Poisson process with exponential jumps. We consider the same stochastic game but driven by a spectrally positive Lévy process. We...

Let M=(Mt)t=0 be any continuous real-valued stochastic process. We prove that if there exists a sequence (an)n=1 of real numbers which converges to 0 and such that M satisfies the reflection property at all levels an and 2an with n=1, then M is an Ocone local martingale with respect to its...

We first give an interpretation for the conditioning to stay positive (respectively, to die at 0) for a large class of Lévy processes starting at x 0. Next, we specify the laws of the pre-minimum and post-minimum parts of a Lévy process conditioned to stay positive. We show that, these parts...

In the present paper we compute the laws of some functionals of doubly perturbed Brownian motion, which is the solution of the equation Xt=Bt+[alpha] sups[less-than-or-equals, slant]t Xs+[beta] infs[less-than-or-equals, slant]t Xs, where [alpha],[beta]1, and B is a real Brownian motion. We first...

We develop an idea of Evans and O'Connell (1994) [13], Engländer and Pinsky (1999) [10] and Duquesne and Winkel (2007) [4] by giving a pathwise construction of the so-called 'backbone' decomposition for supercritical superprocesses. Our results also complement a related result for critical...

We consider the Russian option introduced by Shepp and Shiryayev (Ann. Appl. Probab. 3 (1993) 631, Theory Probab. Appl. 39 (1995) 103) but with finite expiry and show that its space-time value function characterizes the unique solution to a free boundary problem. Further, using a method of...

In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Lévy processes that is based on the Wiener–Hopf decomposition. We pursue this idea further by combining their technique with the recently introduced multilevel Monte Carlo methodology....

In the spirit of Duquesne and Winkel (2007) and Berestycki et al. (2011), we show that supercritical continuous-state branching process with a general branching mechanism and general immigration mechanism is equivalent in law to a continuous-time Galton–Watson process with immigration (with...