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UID:www.tcs.tifr.res.in/event/68
DTSTAMP:20230914T125909Z
SUMMARY:Incorporating Views in Mathematical Models: An Approach Based on En
tropy
DESCRIPTION:Speaker: Santanu Dey\nSchool of Technology and Computer Science
\nTata Institute of Fundamental Research\nHomi Bhabha Road\n\nAbstract: \n
A mathematical model based on historical data or general past experience m
ay at times be an unsatisfactory model for the future. One way to come up
with a more accurate model is to explicitly incorporate in it views that a
re believed to better reflect the future. We address this issue by letting
$\\\\mu$ denote the original probability measure of a mathematical model.
We then search for a probability measure $\\\\nu$ that minimizes a distan
ce measure with respect to $\\\\mu$ and satisfies certain user specified v
iews or constraints. We consider Kullbach-Leibler distance as well as othe
r $f$-divergences as measures of distance between probability measures. We
show that under the KL distance\, our optimization problem may lack a clo
sed form solution when views involve fat tailed distributions. This drawba
ck may be corrected if a ``polynomial-divergence is used. We also discuss
the optimal solution structure under these divergences when the views inc
lude those on marginal probabilities associated with the original probabil
ity measure. We apply these results to the area of portfolio optimization
where we note that a reasonable view that a particular portfolio of assets
has heavy tailed losses leads to a more realistic model through our appro
ach.\n
URL:https://www.tcs.tifr.res.in/web/events/68
DTSTART;VALUE=DATE:20100209
LOCATION:A-212 (STCS Seminar Room)
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