Mathematics and Economics

Bubbles and Crashes: The Local Martingale Characterization of Asset Price Bubbles

In Bubbles and Crashes, Economics, Finance, Mathematics on July 9, 2013 at 2:57 pm

We resume our Bubbles and Crashes series with this post discussing the recent influential works of Robert Jarrow and Phillip Protter on the characterization of bubbles as Local Martingales: The Local Martingale Characterization of Bubbles pdf

CCAPM II: Returns Formulation and the Mean-Variance Frontier

In Asset Pricing Reading Group, Economics, Finance on March 29, 2011 at 1:58 am

Due to technical issues on getting our figure and latex to display and compile on wordpress, we will temporarily include a pdf version of this post: CAPM II: Returns & MVF. We hope to resolve this issue and post in our usual format soon.

Bubbles and Crashes: A Survey of the Efficient Market Hypothesis, Part II

In Bubbles and Crashes, Economics, Finance on February 12, 2011 at 3:48 pm

1. Empirical Tests of the Efficient Market Hypothesis and their Results

The models developed so far provide the theoretic basis for our study. We have clearly defined efficient markets and discussed a paradox in their construction, the joint hypothesis problem. We have used the language of probability theory to imbed rigor into our definition. But, we also find that much of the inspiration for these definitions arose from experience. Germinated by a broad intuition for the structure of asset returns and supported by practical experience with traders and trading, the theory is something of a hybrid: equal parts practice and principle. It was sculpted by finely-tuned economic insight, and followed statistical study or grew alongside it. Mathematical rigor was one fiber in the thread of its development.

Historically, the empirical study of the efficient market hypothesis focused on whether prices fully reflect particular subsets of information, while the unpredictability of stock market returns played a lesser role. Weaker forms of the EMH were tested first. The first subset of information considered was that of past prices, and financial economists sought to determine the validity of the weak form efficient market hypothesis. The next subset of information considered concerned the speed at which asset prices adjusted to news and other information as well as past prices; these studies tested the semi-strong form of the hypothesis. Later work considered past prices, fundamental data, news, and insider information, in an attempt to study the strong form efficient market hypothesis.

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