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UID:www.tcs.tifr.res.in/event/893
DTSTAMP:20230914T125942Z
SUMMARY:Quadratic Loss Minimization with Portfolio and Intertemporal Wealth
Constraints
DESCRIPTION:Speaker: Andrew Heunis (Dept. Electrical & Computer Engineering
\nUniversity of Waterloo\nWaterloo\, Ontario N2L 3G1\, Canada)\n\nAbstract
: \nWe address a problem of stochastic optimal control motivated by portf
olio optimization in mathematical finance\, the goal of which is to minim
ize the expected value of a general quadratic loss function of the wealt
h at close of trade when there is a specified convex constraint on the po
rtfolio\, together with a specified almost-sure lower-bound on intertem
poral wealth over the full trading interval. In the parlance of optimal c
ontrol this problem exhibits the combination of a control constraint (na
mely the portfolio constraint) together with an almost-sure state constra
int (namely the stipulated lower-bound on the wealth process over the tra
ding interval). General optimal control problems with this combination of
constraints are known to be quite challenging\, not least because the La
grange multipliers appropriate to such constraints are far from evident.
The problem that we address has the additional property of being convex\
, and this is key to the application of an ingenious variational method
of R.T. Rockafellar for abstract convex optimization which leads to a vec
tor space of dual variables\, together with a dual functional on the spac
e of dual variables\, such that the dual problem of maximizing the dual
functional is guaranteed to have a solution (or Lagrange multiplier) whe
n the intertemporal state constraint satisfies a simple and natural Slate
r condition. This yields necessary and sufficient conditions for the opt
imality of a candidate portfolio (i.e. control) process\, as well as the
construction (in principle!) of an optimal portfolio.\n\nBio: Andrew Heun
is was born in Johannesburg\, South Africa\, and educated at the Universit
y of the Witwatersrand\, Johannesburg\, and Imperial College\, London\, re
ceiving the PhD degree in Electrical Engineering from the latter instituti
on in 1984. Since 1985 he has been at the Department of Electrical & Compu
ter Engineering\, University of Waterloo\, Ontario\, Canada. During 1992 h
e was Chercheur Invite at IRISA/INRIA\, Rennes\, France. His main interest
s are in applied probability\, with particular focus on limit theorems (fo
r system identification\, averaging principles and recursive stochastic al
gorithms)\, nonlinear filtering\, and more recently\, problems of stochast
ic optimal control motivated particularly by portfolio optimization in mat
hematical finance.\n
URL:https://www.tcs.tifr.res.in/web/events/893
DTSTART;TZID=Asia/Kolkata:20180724T160000
DTEND;TZID=Asia/Kolkata:20180724T170000
LOCATION:A-201 (STCS Seminar Room)
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