CU Graduate Mathematics Society

9:05 (MR14) Colm Bates (cwb33) Security Pricing in an Optimal Contract Setting

We introduce the idea of
the Principal Agent Problem in a continuous time setting. The agent is
hired by a principal to control and report cash flows from a project where
the principal is unable to observe the internal workings of the project.
This can be made analogous to shareholders and banks (principals) holding
a stake (equity and debt) in a company run by directors (agents). We seek
to find the optimal way to pay the agent in order to incentivitise her,
by means of a contract, to report cash flows truthfully. This contract can
be implemented by offering securities to various parties involved in the
model, which given the optimality of the contract allow the securities to
be priced.

10:00 (MR14) Raphael Assier (rca32) Orthogonal polynomials and their link with Julia sets

This talk will develop the basic generic theory of orthogonal
polynomials on the real axis, in order to be able to present the
beautiful Favard theorem. A generalization on the concept of orthogonal
polynomials on a complex contour will also be developed. A particular
interest will be put on the family formed by the iterates of a complex
polynomial T. This will lead to an orthogonal polynomial sequence which
is orthogonal on the Julia set generated by T.

11:10 (MR15) Zhou Feng (zf216) P > N Problems: A Brief Overview

We often aim to elicit the relationship between a response variable and a
number 'p' of inputs using an amount 'n' of data. In traditional
statistics, we hope to have a large amount of data, typically much larger
than p. However, in many real world situations, the reverse is true. It
turns out that a variety of methods exist and are being developed that can
deal with this situation - at least to some degree.

This talk will discuss some of them, and their performance.
Non-statisticians welcome, as the talk will be mostly non-technical, with
proofs omitted.

12:05 (MR15) Adam Fuller (af381) Free Probability Theory

The tools of Free Probability Theory were developed by
Voiculescu in the 1980s when studying the structure of the von Neumann
algebra generated by left regular representation of a free group. The
subject has been shown to have applications in an array of areas including
the theory of random matrices and the theory of large deviations in
classical probability.

In my talk I plan to give a brief introduction to the subject, stating the
key definitions and some key results. I will also, when possible, point out
the analogies between free probability theory and classical probability
theory.

9:05 (MR14) Colm Bates (cwb33) Security Pricing in an Optimal Contract Setting

• Grossman, S.J. and Hart, O.D. (1983)"An Analysis of the Principal Agent
  Problem", Econometrica
• DeMarzo, P. and Fishman, M. (2003) "Optimal Long-Term Financial Contracting
  with Privately Observed Cash Flows", Working Paper, Northwestern University
• DeMarzo, P. and Fishman, M. (2006) "Agency and Optimal Investment
  Dynamics", forthcoming, Review of Financial Studies
• DeMarzo, P. and Sannikov, Y. (2006) "A Continuous-Time Agency Model of
  Optimal Contracting and Capital Structure",
• Tchistyi, A. (2005), "Security Design with Correlated Hidden Cash Flows:
  The Op- timality of Performance Pricing", Ph.D. dissertation, Stanford
  University