7,637 research outputs found
Drichlet forms for Poisson measures and L\'evy processes : the lent particle method
We present a new approach to absolute continuity of laws of Poisson
functionals. The theoretical framework is that of local Dirichlet forms as a
tool to study probability spaces. The method gives rise to a new explicit
calculus that we show first on some simple examples : it consists in adding a
particle and taking it back after computing the gradient. Then we apply it to
SDE's driven by Poisson measure
A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
The aim of this work is to evaluate the cheapest superreplication price of a
general (possibly path-dependent) European contingent claim in a context where
the model is uncertain. This setting is a generalization of the uncertain
volatility model (UVM) introduced in by Avellaneda, Levy and Paras. The
uncertainty is specified by a family of martingale probability measures which
may not be dominated. We obtain a partial characterization result and a full
characterization which extends Avellaneda, Levy and Paras results in the UVM
case.Comment: Published at http://dx.doi.org/10.1214/105051606000000169 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Energy image density property and the lent particle method for Poisson measures
We introduce a new approach to absolute continuity of laws of Poisson
functionals. It is based on the {\it energy image density} property for
Dirichlet forms and on what we call {\it the lent particle method} which
consists in adding a particle and taking it back after some calculation.Comment: 29
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