Exponential Functionals of Brownian Motion and Related Processes

By Marc Yor. 2001

332 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/3db7313c6b1c3bb6e15ac64ea1efe4bcab6166f4

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Citations in the corpus

Distribution of the time to explosion for one-dimensional diffusions (2013, background): “Alternatively, Proposition 6.1 in Yor (2001) yields the representation of the explosion time S as in (6.10) by using the identity in (6.7) but now via a representation of negative powers as an integral of exponentials.”
Bessel processes, the integral of geometric Brownian motion, and Asian options (2003, methodology): “This approach, using the Laplace transform and based on Bessel processes, has been found by Yor to open many surprising vistas on the processes A and their applications; see in particular [32].”
The log-normal approximation in financial and other computations (2004, methodology): “This transformation has been used elsewhere by Yor (including many of the papers reproduced in Yor (2001)) and by this author, Dufresne (2000), (2001a), (2001b).”
Exponential functionals of Levy processes (2005, background): “2004/04/05 file: expfunc.tex date: December 13, 2004 [67]) is equivalent to the knowledge of the law of R t 0 exp( − ξ s ) ds , for ﬁxed t ; an important reduction of the problem consists in replacing t by an exponential time θ , which is independent of ξ (in other words, one kills the L´evy…”
Law of the absorption time of some positive self-similar Markov processes (2009, result): “In the former case, several proofs can be found in the literature, see for instance the excellent monograph of Yor [45] and the more recent survey papers of Matsumoto and Yor [26] and [27].”
Generalised Ornstein-Uhlenbeck Processes and the Convergence of Levy Integrals (2005, background): “[9], [13], [39], [40], [ 41 ] and others investigate this in particular when the integrator and/or integrand are Brownian, giving detailed distributional information (or even an explicit expression for the distribution).”
Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes (2005, neutral): “Yor [30, 31]), insurance and perpetuities (e.”
Differential equations and asymptotic solutions for arithmetic Asian options: ‘Black–Scholes formulae’ for Asian rate calls (2008, positive): “2 A simple derivation of the Geman–Yor formula We can now give a simple derivation of the Geman–Yor model for Asian call option prices [4], but see also [25].”
Exponential functionals of Brownian motion, I: Probability laws at fixed time (2005, methodology): “Moreover, since a probabilistic proof is given in [69], which is also found in [66], we have chosen to give a proof based on the general theory of the Sturm-Liouville operators.”
Tail asymptotics for exponential function-als of L evy processes (2006, neutral): “A recent monograph devoted to such exponential functionals is [32].”
On Exponential Functionals of Lévy Processes (2013, background): “Key words and phrases. generalized Ornstein-Uhlenbeck process, Lévy process, Feller process, infinitesimal generator, integral mapping, stationarity”