June 18, 2002
16:30-18:00, TU FH, Turm A, 6. Stock, Seminarraum 107
Conditioned Stochastic Differential Equations -
Applications to Finance
FABRICE BAUDOIN (Universit´es Paris 6 et Paris 7)
(1) We generalize the notion of Brownian bridge. More precisely, we
study a standard Brownian motion for which a certain functional is
conditioned to follow a given law. Such processes appear as weak
solutions of stochastic differential equations that we call
conditioned stochastic differential equations. The link with the
theory of initial enlargement of filtration is made and after a
general presentation several examples are studied: the conditioning of
a standard Brownian motion (and more generally of a Markov
diffusion) by its value at a given date, and the conditioning of a
standard Brownian motion by its first hitting time of a given level.
(2) As an application, we introduce the notion of weak information on
a complete or incomplete market, and we give a "quantitative" value to
this weak information.
(3) As the end of the talk, we will go one step further by considering
a flow of information: as the price process is revealed, the weak
anticipation is updated.