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SUMMARY:Optimal stopping of a Hilbert space valued diffusion - Dr Tiziano 
 De Angelis\, (University of Manchester)
DTSTART:20121024T150000Z
DTEND:20121024T160000Z
UID:TALK39701@talks.cam.ac.uk
CONTACT:Kevin Crooks
DESCRIPTION:A finite horizon optimal stopping problem for an infinite dime
 nsional diffusion X is analyzed by means of variational techniques. The di
 ffusion is driven by a SDE on a Hilbert space H with a non-linear diffusio
 n coefficient \\sigma(X) and a generic unbounded operator A in the drift t
 erm. When the gain function \\Psi is time-dependent and fulfills mild regu
 larity assumptions\, the value function V of the optimal stopping problem 
 is shown to solve an infinite-dimensional\, parabolic\, degenerate variati
 onal inequality on an unbounded domain. Once the coefficient\\sigma(X) 
 is specified\, the solution of the variational problem is found in a suita
 ble Banach space B fully characterized in terms of a Gaussian measure \\mu
 .\nThis work provides the infinite-dimensional counterpart\, in the spirit
  of Bensoussan and Lions [1]\, of well-known results on optimal stopping t
 heory and variational inequalities in R^n. These results may be useful in 
 several fields\, as in mathematical finance when pricing American options 
 in the HJM model.
LOCATION:MR14\, Centre for Mathematical Sciences
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