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Exponential functionals of Brownian motion and related processes. (English) Zbl 0999.60004
Springer Finance. Berlin: Springer. ix, 205 p. DM 96.19; sFr 85.07; £33.00; $ 49.95 (2001).
This book is a collection of ten papers on the law of certain functionals of geometric Brownian motion. These papers are supplemented by an introduction explaining the role of these functionals in Finance and in Insurance. The volume combines a great variety of different techniques, especially from Stochastic Analysis, and wonderfully illustrates their applicability. To a large extent the material has been reviewed before in Zentralblatt so that for the details it may suffice to refer to [J. Appl. Probab. 29, No. 1, 202-208 (1992; Zbl 0758.60085), Adv. Appl. Probab. 24, No. 3, 509-531 (1992; Zbl 0765.60084); C. R. Acad. Sci., Paris, Sér. I 314, No. 6, 471-474 (1992; Zbl 0759.60084), ibid. 314, No. 12, 951-956 (1992; Zbl 0751.60076), Math. Finance 3, No. 4, 349-375 (1993; Zbl 0884.90029), Insur. Math. Econ. 13, No. 1, 23-34 (1993; Zbl 0792.60074), Stochastics Stochastics Rep. 47, No. 1/2, 71-101 (1994; Zbl 0830.60072), Math. Finance 3, No. 2, 231-240 (1993; Zbl 0884.90056) and J. Appl. Probab. 35, No. 2, 255-271 (1998; Zbl 0929.60063)]. Some of these papers are made available in English for the first time. They are supplemented by an updated list of references and a short review of further progress made since publication of the presented results.
MSC:
60-06Proceedings of conferences (probability theory)
60H30Applications of stochastic analysis
60J65Brownian motion
91B28Finance etc. (MSC2000)
60J25Continuous-time Markov processes on general state spaces