fall 2012

Derivative Securities – Fall 2012

(a) The link between risk-neutral expectations and PDE’s. We have discussed two apparently different approaches to the valuation of a European option: (i) take the discounted risk-neutral expected payoff, or (ii) solve the Black-Scholes PDE. Let’s show now that these two approaches are equivalent. First, consider options on a forward price. We saw long ago that in the discrete time setting, the...

Usc Seminar : Fall 2012

This is an introduction to vertex operator algebras and related topics.

Algebra Prelim Fall 2012

fall & winter 2012

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Advanced Complexity Theory Fall 2012 Lecture 15 — November 1 , 2012

Q: Why are we using circuit lower bounds here, as opposed to a claim such as E ̸⊆ P for example? A: The proof of the Nisan-Wigderson pseudorandom generator relies on nonuniformity, by showing that distinguishing a pseudorandom generator implies a circuit for solving a hard problem – this reduction involves hardwiring advice into a circuit in order to solve the hard problem. A contradiction requi...

Jeffrey R. Haack — Research Statement — Fall 2012

My research focuses on scientific computing and kinetic equations. More specifically I develop and analyze numerical methods for solving the Boltzmann transport equation and similar kinetic models, as well as their application to high performance computing resources. My work is supported by NSF-DMS Grant 1217254 “Accurate high performance computing for nonlinear collisional kinetic theory”, (20...