Penalization of the Wiener measure and principal values
Intégrales stochastiques de processus anticipants et projections duales prévisibles.
We define a stochastic anticipating integral δμ with respect to Brownian motion, associated to a non adapted increasing process (μt), with dual projection t. The integral δμ(u) of an anticipating process (ut) satisfies: for every bounded predictable process ft, E [ (∫ fsdBs ) δμ(u) ] = E [ ∫ fsus...
On symmetric stable random variables and matrix transposition
On certain Markov processes attached to exponential functionals of Brownian motion: application to Asian options.
We obtain a closed formula for the Laplace transform of the first moment of certain exponential functionals of Brownian motion with drift, which gives the price of Asian options. The proof relies on an identity in law between the average on [0,t] of a geometric Brownian motion and the value at time t of a Markov process, for which we can compute explicitly the resolvent.
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