Next Talk
 Speaker: 
Petter Kolm 
 Title: 
Multiperiod Portfolio Selection and Bayesian Dynamic Models 
 Date and time: 
December 2, 1:00 p.m. (light refreshments at 12:45 p.m.) 
 Venue: 
WWH 1302

Abstract
We describe a novel approach to the study of multiperiod portfolio selection problems with time varying alphas, trading costs, and constraints. We show that, to each multiperiod portfolio optimization problem, one may associate a “dual” Bayesian dynamic model. The dual model is constructed so that the most likely sequence of hidden states is the trading path which optimizes expected utility of the portfolio. The existence of such a model has numerous implications, both theoretical and computational. Sophisticated computational tools developed for Bayesian state estimation can be brought to bear on the problem, and the intuitive theoretical structure attained by recasting the problem as a hidden state estimation problem allows for easy generalization to other problems in finance. Time permitting, we discuss several applications to this approach.
This is joint work with Gordon Ritter.
This seminar is meant to benefit young mathematicians, particularly graduate students and postdocs.
It aims to accomplish the following:
 provide a venue for talks that young mathematicians will understand
 expose students to areas of research at the Courant Institute
The research talks should be fairly introductory and accessible to students and nonspecialists in the audience.
Schedule Fall 2016
October 7
 Speaker: 
Carlos FernandezGranda 
 Title:  From Seismology to Compressed Sensing and Back, a Brief History of OptimizationBased Signal Processing 

 
Abstract
In this talk we provide an overview of the history of l1norm minimization applied to underdetermined inverse problems. In the 70s and 80s geophysicists proposed using l1norm minimization for deconvolution from bandpass data in reflection seismography. In the 2000s, inspired by this approach and by magnetic resonance imaging, a method to provably recover sparse signals from random projections, known as compressed sensing, was developed. Theoretical insights used to analyze compressed sensing have recently been adapted to understand the potential and limitations of l1norm minimization for deterministic problems. These include superresolution from lowpass data and the deconvolution problem that originally motivated the geophysicists. 

October 28
 Speaker: 
John Rinzel 
 Title:  Bistable Dynamics of Perceiving Ambiguous Stimuli 

 
Abstract
When experiencing an ambiguous sensory stimulus (e.g., the vasefaces image), subjects may report random alternations (time scale, seconds) between the possible interpretations. I will describe dynamical models for neuronal populations that compete through mutual inhibition for dominance  showing alternations, behaving as noisy oscillators or as multistable systems subject to noisedriven switching. In highly idealized formulations networks are percept specific without direct representation of stimulus features. Our recent work involves perception of ambiguous auditory stimuli (e.g., http://auditoryneuroscience.com/topics/streaminggallopingrhythmparadigm ). The models explicitly incorporate tone features  perceptual selectivity is emergent rather than builtin. 

November 4
 Speaker: 
Scott Armstrong 
 Title:  Stochastic homogenization of elliptic equations 

 
Abstract
I will give an overview of some recent results in stochastic homogenization of divergenceform elliptic PDEs and discuss some connections to diffusions in random environments. 

November 18
 Speaker: 
Nan Chen 
 Title:  Predicting the cloud patterns of the MaddenJulian Oscillation through a loworder nonlinear stochastic model 

 
Abstract
We assess the limits of predictability of the largescale cloud
patterns in the boreal winter MaddenJulian Oscillation (MJO) as measured through outgoing longwave radiation (OLR) alone, a proxy for convective activity. A recent advanced nonlinear time series technique, nonlinear Laplacian spectral analysis, is applied to the OLR data to define two spatial modes with high intermittency associated with the boreal winter MJO. A recent datadriven physicsconstrained loworder stochastic modeling procedure is applied to these time series. The result is a fourdimensional nonlinear stochastic model for the two observed OLR variables and two hidden variables involving correlated multiplicative noise defined through energyconserving nonlinear interaction. Systematic calibration via information theory and prediction experiments show the skillful prediction by these models for 40, 25, and 18 days in strong, moderate, and weak MJO winters, respectively. Furthermore, the ensemble spread is an accurate indicator of forecast uncertainty at long lead times.
If time permits, calibration and prediction of another type of the MJO indices with a novel informationtheoretic framework will be briefly mentioned at the end of the talk. The informationtheoretic framework overcomes the fundamental insufficiency of the pathwise RMS error and pattern correlation in capturing the extremely events. The applications to the monsoon intraseasonal variability with spatialtemporal reconstruction will be roughly discussed as well. The mathematical tools developed here are also useful in material science, biological science and neuroscience. 

December 2
 Speaker: 
Petter Kolm 
 Title:  Multiperiod Portfolio Selection and Bayesian Dynamic Models 

 
Abstract
We describe a novel approach to the study of multiperiod portfolio selection problems with time varying alphas, trading costs, and constraints. We show that, to each multiperiod portfolio optimization problem, one may associate a “dual” Bayesian dynamic model. The dual model is constructed so that the most likely sequence of hidden states is the trading path which optimizes expected utility of the portfolio. The existence of such a model has numerous implications, both theoretical and computational. Sophisticated computational tools developed for Bayesian state estimation can be brought to bear on the problem, and the intuitive theoretical structure attained by recasting the problem as a hidden state estimation problem allows for easy generalization to other problems in finance. Time permitting, we discuss several applications to this approach.
This is joint work with Gordon Ritter. 

If you would like to give a talk or ask a question about the seminar,
please contact one of the seminar organizers:
Alexisz Gaal   gaal [at] cims [dot] nyu [dot] edu 
Reza Gheissari   reza [at] cims [dot] nyu [dot] edu 
Previous semesters
Descriptions of earlier talks are
here.
Department of Mathematics
Courant Institute of Mathematical Sciences
New York University
251 Mercer St.
New York, NY 10012