On certain Markov processes attached to exponential functionals of Brownian motion: application to Asian options.

By Catherine Donati-Martin, R. Ghomrasni, Marc Yor. 2001

83 citations recorded by the source corpus.

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Citations in the corpus

Exponential functionals of Brownian motion, II: Some related diffusion processes (2005, methodology): “We next present another proof of Theorem 2.2, following Donati-Martin, Ghomrasni and Yor [16], who have used, as an auxiliary tool, the stochastic process Y (µ)(x) = {Y (µ)t (x)} given by Y (µ) t (x) = exp(2B (µ) t ) ( x+ ∫ t 0 exp(−2B(µ)s )ds ) .”
The integral of geometric Brownian motion (2001, background): “There have been a number of other papers on the same integral functional of Brownian motion, including Yor (1992a), (1992b), (1992c), de Schepper et al. (1992), Carmona et al. (1997), Dufresne (2001) and Donati-Martin et al. (2001).”
PRICING EQUITY DERIVATIVES SUBJECT TO BANKRUPTCY (2006, unknown): “Dufresne’s identity in law (Dufresne 1989, 1990; see also Donati-Martin, Ghomrasni, and Yor 2001) states that, for each fixed t > 0, A(ν)t (law)= X (ν)t , where X (ν)t is the diffusion process (3.4) starting at the origin.”
On the equivalence of floating- and fixed-strike Asian options (2002, background): “Pricing of the fixed-strike Asian has been the subject of much research over the last ten years and academic interest in these options has experienced a revival recently, see Carr and Schröder [6], Donati-Martin, Ghomrasni and Yor [9].”
THE SPECTRAL DECOMPOSITION OF THE OPTION VALUE (2004, background): “and started at the origin at time zero,X0 = 0 (see [21] and references therein).”
Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes (2005, unknown): “Hence we obtain[ e−ξ, Bη ] t = [ − ∫ · 0 e−ξs− dξs, Bη ] t + [F,Bη]t = − ∫ t 0 e−ξs− d[ξ, Bη]s + 0 = − ∫ t 0 e−ξs−d(Cov(Bξ,1, Bη,1)s).”