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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:Çağın Ararat\, Bilkent University\, Turkey\n\nAbstract: The dyn
amic mean-variance problem is a well-studied optimization problem that is k
nown to be time-inconsistent. The main source of time-inconsistency is that
the family of conditional variance functionals indexed by time fails to be
recursive. We consider the mean-variance problem in a discrete-time settin
g and study an auxiliary dynamic vector optimization problem whose objectiv
e function consists of the conditional mean and conditional second moment.
We show that the vector optimization problem satisfies a set-valued dynamic
programming principle and is timeconsistent in a generalized sense. Moreov
er\, its weighted sum scalarizations are closely related to the mean-varian
ce problem through simple nonlinear transformations. This is at the cost of
using stochastic and time-varying weights in the mean-variance problem. We
also discuss the relationship between our results and some recent results
in the literature that discuss the use of time-varying weights under specia
l dynamics. Finally\, in a finite probability space\, we propose a computat
ional procedure that relies on convex vector optimization and convex projec
tion problems\, and we use\nthis procedure to calculate time-consistent sol
utions in concrete market models. Joint work with Seyit Emre Düzoylum (Bilk
ent).
DTEND:20210913T220000Z
DTSTAMP:20211201T150632Z
DTSTART:20210913T210000Z
LOCATION:
SEQUENCE:0
SUMMARY:Mathematical Finance Colloquium: Dynamic mean-variance problem: rec
overing time-consistency
UID:tag:localist.com\,2008:EventInstance_37757731651524
URL:https://calendar.usc.edu/event/mathematical_finance_colloquium_dynamic_
mean-variance_problem_recovering_time-consistency
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