87,437 research outputs found
Optimal multiple stopping time problem
We study the optimal multiple stopping time problem defined for each stopping
time by . The key point is the construction
of a new reward such that the value function also satisfies
.
This new reward is not a right-continuous adapted process as in the
classical case, but a family of random variables. For such a reward, we prove a
new existence result for optimal stopping times under weaker assumptions than
in the classical case. This result is used to prove the existence of optimal
multiple stopping times for by a constructive method. Moreover, under
strong regularity assumptions on , we show that the new reward can
be aggregated by a progressive process. This leads to new applications,
particularly in finance (applications to American options with multiple
exercise times).Comment: Published in at http://dx.doi.org/10.1214/10-AAP727 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Minimal surfaces - variational theory and applications
Minimal surfaces are among the most natural objects in Differential Geometry,
and have been studied for the past 250 years ever since the pioneering work of
Lagrange. The subject is characterized by a profound beauty, but perhaps even
more remarkably, minimal surfaces (or minimal submanifolds) have encountered
striking applications in other fields, like three-dimensional topology,
mathematical physics, conformal geometry, among others. Even though it has been
the subject of intense activity, many basic open problems still remain. In this
lecture we will survey recent advances in this area and discuss some future
directions. We will give special emphasis to the variational aspects of the
theory as well as to the applications to other fields.Comment: Proceedings of the ICM, Seoul 201
Geometric conditions for regularity in a time-minimum problem with constant dynamics
Continuing the earlier research on local well-posedness of a time-minimum problem associated to a closed target set C in a Hilbert space H and a convex constant dynamics F we study the Lipschitz (or, in general, Hölder) regularity of the (unique) point in C achieved from x for a minimal time. As a consequence, smoothness of the value function is proved, and an explicit formula for its derivative is given
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