Abstract
This paper is motivated by questions about averages of stochastic processeswhich originate in mathematical finance, originally in connection with valuing the so-called Asian options. Starting with [M. Yor, {\em Adv. Appl. Probab.}, 24 (1992), pp. 509--531], these questions about exponential functionals of Brownian motion have been studied in terms of Bessel processes using the Hartman--Watson theory of [M. Yor, {\em Z. Wahrsch. Verw. Gebiete}, 53 (1980), pp. 71--95]. Consequences of this approach for valuing Asian options proper have been spelled out in [H. Geman and M. Yor, {\em Math. Finance}, 3 (1993), pp. 349--375] whose Laplace transform results were in fact regarded as a significant advance. Unfortunately, a number of difficulties with the key results of this last paper have surfaced which are now addressed in this paper. One of them in particular is of a principal nature and originates with the Hartman--Watson approach itself: this approach is in general applicable without modifications only if it...
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
