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October 2014

Stochastic Analysis Common-Tom Emmerling (Syracuse University)-Portfolio Balance Effects and the Fed's Large-Scale Asset Purchases
Monday, 10/27/2014 4:00 PM-5:00 PM
Stratton Hall, 308
ABSTRACT: The recent financial crisis brought back into focus the importance of accurately identifying expected returns. The benefit of hindsight offers the judgement that before the financial crisis, investors were far too willing to accept low expected returns for holding risky assets. In its response to the crisis, the Fed enacted the large-scale asset purchase programs (LSAPs) in an effort to bring down long-term yields in fixed income markets. Whereas much of previous research focuses primarily upon its impact to bond yields, changes to expected returns for both bond and equity investors has been largely overlooked. In this talk, I’ll discuss a mechanism by which the Fed’s actions can indirectly change risk premia in outside markets and discuss some preliminary empirical findings in this regard.
For more information, e-mail ma-chair@wpi.edu.

Colloquium-Leonid Manevich (Russian Academy of Sciences)-Energy exchange, localization and transfer in nonlinear oscillatory chains and nanostructures (resonance non-stationary dynamics)
Friday, 10/31/2014 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: A new approach to non-stationary nonlinear dynamics, based on the concept of Limiting Phase Trajectories (LPTs) is presented. The systems under consideration are finite nonlinear oscillatory chains which can be identified, e.g., as the dynamical models of mechanical structures, polymer macromolecules or carbon nanotubes (CNTs). The LPT describes the most intensive energy exchange between weakly coupled parts of the system which can be considered as effective particles (EPs). They represent the excitations alternative to Nonlinear Normal Modes (NNMs) which are not involved into the processes with the energy exchange and demonstrate the wave-like behavior. It is possible to speak about distinctive wave-particle duality (WPD) in the framework of classical mechanics, and manifestation of particle-like or wave-like behavior depends on the initial conditions or on the type of attractor ( it may be NNM as well as LPT).
Due introducing the EPs the physical nature of the WPD becomes apparent (when the particles themselves are strongly coupled, and the NNMs are resonant, that means their coherence, the EPs are weakly coupled). The transition from the most intensive energy exchange to the energy localization in the part of the system is also naturally described in terms of EPs and LPTs.
The presented approach has significant applications connected with elaboration of the energy traps, synchronization of oscillators, providing the energy exchange and localization in CNTs etc., which will be briefly described.

For more information, e-mail ma-chair@wpi.edu.

November 2014

Stochastic Analysis Common-Xiang Yu (University of Michigan)-Optimal Investment with Unbounded Random Endowments and Transaction Costs: Duality Theory and Connections to the Shadow Price Process
Monday, 11/3/2014 4:00 PM-5:00 PM
Stratton Hall, 308
ABSTRACT: We study the utility maximization problem on terminal wealth with transaction costs and random endowments. To deal with unbounded random payoffs from some illiquid claims, we propose to work with the acceptable portfolios defined via the consistence price system such that the liquidation value processes maintain above some stochastic process thresholds. In the market consisting of one bond and one cadlag risky asset with small bid-ask spread, we obtain a type of super-hedging result for some workable contingent claims. Based on this characterization of the primal space, the existence and uniqueness of the optimal portfolio are established using convex analysis. As an application of the duality theory, the existence of a shadow price process with random endowments is investigated in a general sandwiched form as well as in the classical sense using acceptable portfolios.
For more information, e-mail ma-chair@wpi.edu.

Colloquium-Gwen Spencer (Smith College)-Influence Beyond Exposure: Tackling an Economic Variant of Seeding Viral Spread
Friday, 11/7/2014 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: The problem of seeding "contagion" in social networks has attracted substantial attention for its connection to viral marketing. Simple information-spread models yield nice mathematical properties that allow theoretical algorithmic traction. This work often points to some form of "exposure" as the best paradigm for designing seed sets. While exposure-based seeding may spread awareness effectively, being aware of a behavior often doesn't result in a decision to adopt it. When environmental economists describe decisions to engage in green behaviors, when sociologists model norm-spread, and when game theorists consider choices to adopt cooperative strategies in repeated-game-play, a common more-complex spread mechanism emerges. What can we learn about how to virally market biking to work, adopting health-related behaviors, and cooperating at an equilibrium that is mutually beneficial?

I'll mention convergence results for this spread mechanism, (daunting) hardness results for the seeding question, and (heartening) computational results from heuristics derived by truncating an exact (inefficient) Integer Program. Compared to exposure-based seeding, the advantage of a seeding paradigm that establishes "critical mass locally" appears largest when the network is highly clustered (as social networks often are).

For more information, e-mail ma-chair@wpi.edu.

Stochastic Analysis Common-Yanlai Chen (UMass Dartmouth)-Certified reduced basis method and reduced collocation method
Monday, 11/10/2014 4:00 PM-5:00 PM
Stratton Hall, 308
ABSTRACT: Models of reduced computational complexity is indispensable in scenarios where a large number of numerical solutions to a parametrized partial differential equation are desired in a fast/real-time fashion. These include simulation-based design, parameter optimization, optimal control, multi-model/scale analysis, uncertainty quantification etc. Thanks to an offline-online procedure and the recognition that the parameter-induced solution manifolds can be well approximated by finite-dimensional spaces, reduced basis method (RBM) and reduced collocation method (RCM) can improve efficiency by several orders of magnitudes. The accuracy of the RBM solution is maintained through a rigorous a posteriori error estimator whose efficient development is critical.

In this talk, I will give a brief introduction of the RBM and discuss recent and ongoing efforts to develop RCM, and the accompanying parametric analytical preconditioning techniques which are capable of improving the quality of the error estimation uniformly on the parameter domain, and speeding up the convergence of the reduced solution to the truth approximation significantly. These results are critical in certifying the accuracy of the reduced model and giving it a reliable predictive value.

For more information, e-mail ma-chair@wpi.edu.

Colloquium-Mert Gürbüzbalaban (MIT)-Title TBA
Friday, 11/14/2014 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.

Colloquium-Camelia Pop (University of Pennsylvania)-Harnack Inequalities for degenerate diffusions
Friday, 11/21/2014 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: We study various probabilistic and analytical properties of a class of degenerate diffusion operators arising in Population Genetics, the so-called generalized Kimura diffusion operators. Our main results is a stochastic representation of weak solutions to a degenerate parabolic equation with singular lower-order coefficients, and the proof of the scale-invariant Harnack inequality for nonnegative solutions to the Kimura parabolic equation. The stochastic representation of solutions that we establish is a considerable generalization of the classical results on Feynman-Kac formulas concerning the assumptions on the degeneracy of the diffusion matrix, the boundedness of the drift coefficients, and on the a priori regularity of the weak solutions.
For more information, e-mail ma-chair@wpi.edu.

Stochastic Analysis Common-Andreea Minca (Cornell University)-Title TBA
Monday, 11/24/2014 4:00 PM-5:00 PM
Stratton Hall, 308
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.

December 2014

Colloquium-Jeremy Tyson (UIUC)-Title TBA
Friday, 12/5/2014 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.

Stochastic Analysis Common-Elise Gourier (Princeton University)-Title TBA
Monday, 12/15/2014 4:00 PM-5:00 PM
Stratton Hall, 308
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.

February 2015

Colloquium-Thaleia Zariphopoulou (UT Austin)-Title TBA
Friday, 2/20/2015 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.

April 2015

Colloquium-Alex Iosevich (University of Rochester)-Title TBA
Friday, 4/10/2015 11:00 AM-12:00 PM
Stratton Hall, 203
ABSTRACT: TBA
For more information, e-mail ma-chair@wpi.edu.

 
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