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Law of the exponential functional of one-sided Lévy processes and Asian options. (English. Abridged French version) Zbl 1162.60015
Summary: The purpose of this note is to describe, in terms of a power series, the distribution function of the exponential functional, taken at some independent exponential time, of a spectrally negative Lévy process \(\xi =(\xi_t,\,t\geq 0\)) with unbounded variation. We also derive a Geman-Yor type formula for Asian option prices in a financial market driven by \(e^\xi \).

MSC:
60G51 Processes with independent increments; Lévy processes
91G20 Derivative securities (option pricing, hedging, etc.)
60E05 Probability distributions: general theory
91G80 Financial applications of other theories
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