T-Space Collection:
http://hdl.handle.net/1807/25335
2014-04-19T22:09:56ZHigh Frequency Trading in a Regime-switching Model
http://hdl.handle.net/1807/25636
Title: High Frequency Trading in a Regime-switching Model
Authors: Jeon, Yoontae
Abstract: One of the most famous problem of finding optimal weight to maximize an agent's expected terminal utility in finance literature is Merton's optimal portfolio problem. Classic solution to this problem is given by stochastic Hamilton-Jacobi-Bellman Equation where we briefly review it in chapter 1. Similar idea has found many applications in other finance literatures and we will focus on its application to the high-frequency trading using limit orders in this thesis. In [1], major analysis using the constant volatility arithmetic Brownian motion stock price model with exponential utility function is described. We re-analyze the solution of HJB equation in this case using different asymptotic expansion. And then, we extend the model to the regime-switching volatility model to capture the status of market more accurately.2011-01-01T15:28:35ZConvergence Results for Rearrangements: Old and New.
http://hdl.handle.net/1807/25582
Title: Convergence Results for Rearrangements: Old and New.
Authors: Fortier, Marc
Abstract: The purpose of this thesis is twofold. On the one hand, it aims to give a thorough review and exposition of current best results regarding approximating the symmetric decreasing rearrangement by polarizations and Steiner symmetrizations. These results include those of Van Schaftingen on explicit universal approximation to the symmetric decreasing rearrangement by sequences of polarizations as well as his results on almost sure convergence of rearrangements to the symmetric decreasing rearrangement. They also include those of Klartag and Milman which yield rates of convergence for Steiner symmetrizations of convex bodies. On the other hand, new results are proven. We extend Van Schaftingen's results on almost sure convergence of polarizations and Steiner symmetrizations by showing that the conditions on the random variables can be weakened without affecting almost sure convergence to the symmetric decreasing rearrangement. Lastly, we derive rates of convergence for polarizations and Steiner symmetrizations of HÃ¶lder continuous functions.2010-12-31T20:34:53ZOn the Plane Fixed Point Problem
http://hdl.handle.net/1807/25445
Title: On the Plane Fixed Point Problem
Authors: Chambers, Gregory
Abstract: Several conjectured and proven generalizations of the Brouwer Fixed Point Theorem are examined, the plane fixed point problem in particular. The difficulties in proving this important conjecture are discussed. It is shown that it is true when strong additional assumptions are made.
Canonical examples are produced which demonstrate the differences between this result and other generalized fixed point
theorems.2010-12-15T16:34:54ZOn Moments of Class Numbers of Real Quadratic Fields
http://hdl.handle.net/1807/24553
Title: On Moments of Class Numbers of Real Quadratic Fields
Authors: Dahl, Alexander Oswald
Abstract: Class numbers of algebraic number fields are central invariants. Once the underlying field has an infinite unit group they behave very irregularly due to a non-trivial regulator. This phenomenon occurs already in the simplest case of real quadratic number fields of which very little is known.
Hooley derived a conjectural formula for the average of class numbers of real quadratic fields. In this thesis we extend his methods to obtain conjectural formulae and bounds for any moment, i.e., the average of an arbitrary real power of class numbers. Our formulae and bounds are based on similar (quite reasonable) assumptions of Hooley's work.
In the final chapter we consider the case of the -1 power from a numerical point of view and develop an efficient algorithm to compute the average for the -1 class number power without computing class numbers.2010-07-22T19:09:26Z