Abstract
Part A of this paper is a transcript of the third author’s lecture at the Bachelier Conference, July 1st, 2000; it is a summary of our joint works on this topic.
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References
L. Alili, D. Dufresne et, M. Yor, Sur l’identité de Bougerol pour les fonctionnelles exponentielles du mouvement, brownien avec drift,, in Exponential Functionals and Principal Values related to Brownian Motion, A collection of research papers, Ed. by M. Yor, Biblioteca de la Revista Matemàtica Iberoamericana, 1997.
L. Chaumont, D.G. Hobson and M. Yor, Some consequences of the cyclic exchangeability property for exponential functionals of Lévy processes, Séni. Prob. XXXV, Lec. Notes Math. 1755, 334–347, Springer-Verlag, 2001.
P. Carmona, F. Petit, and M. Yor, Exponential functionals of Lévy processes, in Lévy Processes: Theory and Applications, ed. by O.E. Barndorff-Nielsen, T. Mikosch and S.I. Resnick, 41–56, Birkhâuser, 2001.
C. Donati-Martin, H. Matsumoto and M. Yor, On striking identities about, the exponential functionals of the Brownian bridge and Brownian motion, Periodica Math. Hung., 41 (2000), 103–119.
C. Donati-Martin, H. Matsumoto and M. Yor, On positive and negative moments of the integral of geometric Brownian motions, Stat,. Prob. Lett,., 49 (2000), 4. 5–52.
D. Dufresne, The distribution of perpetuity, with applications to risk theory and pension funding, Scand. Act,. J., 1990, 39–79.
D. Dufresne, An affine property of the reciprocal Asian option process, Osaka J. Math. 38 (2001), 379–381.
D. Dufresne, Laguerre series for Asian and other options, Math. Finance, 10 (2000), 407–428.
H. Geman and M. Yor, Bessel processes, Asian options, and perpetuities. Math. Finance, 3 (1993), 349–375.
N. O’Connell and M. Yor, Brownian analogues of Burke’s theorem, to appear in Stoch. Proc. Appl., 2001.
K. It,ô and H.P. McKean, Jr., Diffusion Processes and Their Sample Paths, Springer-Ver lag, Berlin, 1965.
D. Lamberton and B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall, London, 1996.
J. Lamperti, Semi-stable Markov processes I, Z.W., 22 (1972), 205–255.
N.N. Lebedev, Special Functions and their Applications, Dover, New York, 1972.
E.H. Lehmann, Testing Statistical Hypotheses, 2nd Ed., Wiley, New York, 1986.
H. Matsumoto and M. Yor, On Bougerol and Dufresne’s identities for exponential Brownian functionals, Proc. Japan Acad., 74 Ser.A (1998), 152–155.
H. Matsumoto and M. Yor, A version of Pitman’s 2M — X theorem for geometric Brownian motions, C. R. Acad. Sc. Paris, 328 (1999), 1067–1074.
H. Matsumoto and M. Yor, A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration, Osaka J. Math. 38 (2001), 383–398.
E.J. Pauwels and L.C.G. Rogers, Skew-product, decompositions of Brownian motions, Geometry of random motion, 237–262, Contemp. Math., 73, AMS, Providence, 1988.
D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 3rd. Ed., Springer-Verlag, Berlin, 1999.
J.P. Serre, Cours d’arithmétique, PUF, 1970.
G.N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge Univ. Press, Cambridge, 1944.
D. Williams, Diffusions, Markov Processes and Martingales, vol. 1: Foundations, Wiley and Sons, New York, 1979.
M. Yor, Sur certaines fonctionnelles exponentielles du mouvement, brownien réel, J. Appl. Prob., 29 (1992), 202–208.
M. Yor, On some exponential functionals of Brownian motion, Adv. Appl. Prob., 24 (1992),.509–531.
M. Yor, From planar Brownian windings t,o Asian options, Insurance Math. Econom., 13 (1993), 23–34.
M. Yor (ed.), Exponential Functionals and Principal Values related to Brownian Motion, A collection of research papers, Biblioteca de la Revista Matemâtica Iberoamericana, 1997.
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Donati-Martin, C., Matsumoto, H., Yor, M. (2002). The Law of Geometric Brownian Motion and its Integral, Revisited; Application to Conditional Moments. In: Geman, H., Madan, D., Pliska, S.R., Vorst, T. (eds) Mathematical Finance — Bachelier Congress 2000. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12429-1_11
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