Title: THE LOG-PERIODIC POWER LAW MODEL: AN EXPLORATION
Abstract:
Over the last two decades, a new financial model has emerged that might explain some of the rare instances of truly extreme volatility in asset prices. This model, known as the Log-Periodic Power Law (LPPL) model or the Johansen-Ledoit-Sornette (JLS) model attempts to diagnose, time, and predict the termination of these bubbles; we caution that there is no academic agreement about the existence or definition of a “bubble”. The creators of the model provide a motivation built upon some natural assumptions including risk-neutral assets, rational expectations, local self-reinforcing imitation, and probabilistic critical times. The model has evolved over time, partially in response to some sound criticism. This dissertation is focused on two criticisms that have not been fully addressed. First, it is unknown whether there exists unique best fits of the JLS model to log-price data. In this dissertation we explore the first level JLS model and analyze its relationship with extreme boundary vectors which serve as the building blocks for increasing concave up log-price paths. Second, it is unknown whether the current method for locating local minima is sufficient. Using numerical analysis, this dissertation uses the Cauchy-Schwarz Theorem and Taylor’s Theorem to find bounds for various moduli of continuity and first and second derivatives of the error of the JLS model fitted to appropriate log-price paths. In addition to discussing these criticisms, the question of the applicability of the JLS model is considered. Without committing ourselves to a definition of a bubble, this dissertation also presents the results of an ongoing test attempting to determine whether the JLS model can be used to generate systematic profits. An experiment using the JLS model on specifically chosen stocks filtered from the New York Stock Exchange (NYSE) is detailed along with a step-by-step procedure to determine specific dates on which to utilize a trading strategy.
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Antonella Perucca (University of Regensburg), Reductions of algebraic numbers
Number theory talk, accessible to all graduate students. Join us! Abstract: We start by considering the reductions of the integers modulo the various prime numbers. More precisely, we investigate the multiplicative order of the reductions of an integer.
We then generalize this setting to number fields and illustrate some results which are joint work with Christophe Debry.
Speaker: William Stein (SageMath, Inc. & University of Washington)
Title: What is SageMath good for?
Abstract: Answer – almost everything you do. I will talk about how you can use SageMath in teaching and research. In particular, how to use Sage to support courses involving computation, to help in collaborative writing of LaTeX documents, to contribute and improve peer reviewed implementations of algorithms, and to explore new mathematics.