912 research outputs found
Thin times and random times' decomposition
The paper studies thin times which are random times whose graph is contained
in a countable union of the graphs of stopping times with respect to a
reference filtration . We show that a generic random time can be
decomposed into thin and thick parts, where the second is a random time
avoiding all -stopping times. Then, for a given random time ,
we introduce , the smallest right-continuous filtration
containing and making a stopping time, and we show that, for
a thin time , each -martingale is an -semimartingale, i.e., the hypothesis for
holds. We present applications to honest times,
which can be seen as last passage times, showing classes of filtrations which
can only support thin honest times, or can accommodate thick honest times as
well
Minimal -martingale measures for exponential L\'evy processes
Let be a multidimensional L\'evy process under in its own filtration.
The -minimal martingale measure is defined as that equivalent local
martingale measure for which minimizes the -divergence
for fixed . We give necessary and
sufficient conditions for the existence of and an explicit formula for
its density. For , we relate the sufficient conditions to the structure
condition and discuss when the former are also necessary. Moreover, we show
that converges for in entropy to the minimal entropy
martingale measure.Comment: Published in at http://dx.doi.org/10.1214/07-AAP439 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Dynamics of multivariate default system in random environment
We consider a multivariate default system where random environmental
information is available. We study the dynamics of the system in a general
setting and adopt the point of view of change of probability measures. We also
make a link with the density approach in the credit risk modelling. In the
particular case where no environmental information is concerned, we pay a
special attention to the phenomenon of system weakened by failures as in the
classical reliability system
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