Advances in Financial Mathematics

Session Organizers: 

Gunduz Caginalp, University of Pittsburgh
Ahmet Duran, University of Michigan-Ann Arbor

6 Speakers (Meyer, Goodman, Stojanovic, Zhang, Sturm, Duran)

Principal Component Analysis of Forward Interest Rates
Abstract: Observations of forward interest rates determine a high-dimensional covariance matrix that summarizes the volatility of yields within a central bank's bond market.  A principal component analysis of these rates, using data from different decades and from different countries, displays a common pattern under the assumption of a Gaussian trading noise.  I will describe this (well-known) pattern and will also describe a mathematical obstacle which has prevented any viable model from expressing the PCA results.  Then I show that, by conditioning on certain favorable market events, we can produce three factor models which have the volatility characteristics of PC market-data analyses. (Received January 28, 2008)

Quantitative Equity: Dividend Policy, Risk Premium, and Market Share Dynamics
Abstract: We employ the recent theory of pricing of liquid financial contracts in multi-factor incomplete markets with risk premium determination to value equity. In particular the so called "Dividend Puzzle" of F. Black in regard to the Miller-Modigliani theorem of dividend policy irrelevancy, is resolved quantitatively. We further study the firm's market share dynamics effect on the equity value. Finally, some empirical results are presented. (Received April 9, 2008)

The Risk of Bankruptcy in Long-term Investment

Abstract: In recent years, various continuous-time strategies in portfolio management have been developed with different objectives. However the risks associated with these strategies are not well understood. We focus on one particular measure of risk in this talk, namely the probability of bankruptcy occurring while applying these strategies. We demonstrate that applications of untamed strategies in long-term investments always lead to sure bankruptcy. This is true even when the target-return rate is only slightly above the risk-free interest rate. For tamed strategies,  if the target-return rate is set above certain critical value, then the probability of being in bankruptcy will be one hundred percent for a long-term investor. Empirical study based on the market data confirms these findings. (Received April 10, 2008)

The 52-week high strategy: Momentum and Overreaction in Large Firm Stocks

Abstract: Prior studies have documented momentum profits to stock portfolios formed from 52-week highs in prices.  In this study, I primarily examine the pattern of returns to portfolios formed from other highs besides the 52-week high and from the time interval between current prices and the prior high.  I find evidence suggesting that investors attach value to prior highs and lows besides the 52-week high/low, but the 52-week high/low appears to have more value than the others.  My results imply that prior price extremes contain information about future returns, and present a challenge to market efficiency. (Received May 7, 2008)

Quantitative Behavioral Finance and Out-of-sample Prediction via Asset Flow Differential Equations

Quantitative behavioral finance is a new discipline that uses mathematical and statistical methodology to understand behavioral (cognitive and emotional) biases in conjunction with valuation. A system of nonlinear asset flow differential equations (AFDE) incorporates behavioral concepts with the finiteness of assets and microeconomic principles. They have been developed and analyzed asymptotically by Caginalp and collaborators since 1989. I will focus on how the elimination of "noise" or changes in valuation and an inverse problem involving parameter optimization for AFDE can be used in order to forecast near term market returns by following out-of-sample procedure.