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Description of Exponential Functionals of Brownian Motion and Related Processes |
This volume collects papers about the laws of geometric Brownian motions and their time-integrals, written by the author and coauthors between 1988 and 1998. These functionals play an important role in Mathematical Finance, as well as in (probabilistic) studies related to hyperbolic geometry, and also to random media. Throughout the volume, connections with more recent studies involving exponential functionals of Levy processes are indicated. Some papers originally published in French are made available in English for the first time.
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Contents of Exponential Functionals of Brownian Motion and Related Processes |
Preface
0. Functionals of Brownian Motion in Finance and in Insurance
by Helyette Geman
1. On Certain Exponential Functionals of Real-Valued Brownian Motion
J. Appl. Prob. 29 (1992)
2. On Some Exponential Functionals of Brownian Motion
Adv. Appl. Prob. 24 (1992)
3. Some Relations between Bessel Processes, Asian Options and Confluent Hypergeometric Functions
C.R. Acad. Sci., Paris, Ser. I 314 (1992), 471–474 (with Helyette Geman)
4. The Laws of Exponential Functionals of Brownian Motion, Taken at Various Random Times
C.R. Acad. Sci., Paris, Ser. I 314 (1992)
5. Bessel Processes, Asian Options, and Perpetuities
Mathematical Finance, Vol. 3, No. 4 (October 1993), (with Helyette Geman)
6. Further Results on Exponential Functionals of Brownian Motion
7. From Planar Brownian Windings to Asian Options
Insurance: Mathematics and Economics 13 (1993)
8. On Exponential Functionals of Certain Levy Processes
Stochastics and Stochastic Rep. 47 (1994), (with P. Carmona and F. Petit)
9. On Some Exponential-integral Functionals of Bessel Processes
Mathematical Finance, Vol. 3, No. 2 (April 1993)
10. Exponential Functionals of Brownian Motion and Disordered Systems
J. App. Prob. 35 (1998), (with A. Comtet and C. Monthus)
Index
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