Mathematical Finance Colloquium: Dynamic mean-variance problem: recovering time-consistency

Monday, September 13 at 2:00pm to 3:00pm

This is a past event.
Virtual Event


Çağın Ararat, Bilkent University, Turkey

Abstract: The dynamic mean-variance problem is a well-studied optimization problem that is known 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 setting and study an auxiliary dynamic vector optimization problem whose objective 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. Moreover, its weighted sum scalarizations are closely related to the mean-variance 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 special dynamics. Finally, in a finite probability space, we propose a computational procedure that relies on convex vector optimization and convex projection problems, and we use
this procedure to calculate time-consistent solutions in concrete market models. Joint work with Seyit Emre Düzoylum (Bilkent).

 

Dial-In Information

Join Zoom Meeting: https://usc.zoom.us/j/99844331662?pwd=eUpTMUVSTkFVaUZock5FamV2MS9Idz09

Meeting ID: 998 4433 1662
Passcode: 349982              

 

Event Type

Lecture / Talk / Workshop

Department
Mathematics
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