Universal Laws and Economic Phenomena

This is a short commentary piece that discusses how the methods used in the natural sciences can apply to economics in general and financial markets specifically.Comment: 3 pages, 1 figur

The Doomsday Argument in Many Worlds

You and I are highly unlikely to exist in a civilization that has produced only 70 billion people, yet we find ourselves in just such a civilization. Our circumstance, which seems difficult to explain, is easily accounted for if (1) many other civilizations exist and if (2) nearly all of these civilizations (including our own) die out sooner than usually thought, i.e., before trillions of people are produced. Because the combination of (1) and (2) make our situation likely and alternatives do not, we should drastically increase our belief that (1) and (2) are true. These results follow immediately when considering a many worlds version of the "Doomsday Argument" and are immune to the main criticism of the original Doomsday Argument.Comment: 18 page

Seiberg-Witten and Gromov invariants for self-dual harmonic 2-forms

This is the sequel to the author's previous paper which gives an extension of Taubes' "SW=Gr" theorem to non-symplectic 4-manifolds. The main result of this paper asserts the following. Whenever the Seiberg-Witten invariants are defined over a closed minimal 4-manifold X, they are equivalent modulo 2 to "near-symplectic" Gromov invariants in the presence of certain self-dual harmonic 2-forms on X. A version for non-minimal 4-manifolds is also proved. A corollary to circle-valued Morse theory on 3-manifolds is also announced, recovering a result of Hutchings-Lee-Turaev about the 3-dimensional Seiberg-Witten invariants.Comment: 41 pages. Comments desired; to be submitte

Simulating the Synchronizing Behavior of High-Frequency Trading in Multiple Markets

Nearly one-half of all trades in financial markets are executed by high-speed, autonomous computer programs -- a type of trading often called high-frequency trading (HFT). Although evidence suggests that HFT increases the efficiency of markets, it is unclear how or why it produces this outcome. Here we create a simple model to study the impact of HFT on investors who trade similar securities in different markets. We show that HFT can improve liquidity by allowing more transactions to take place without adversely affecting pricing or volatility. In the model, HFT synchronizes the prices of the securities, which allows buyers and sellers to find one another across markets and increases the likelihood of competitive orders being filled.Comment: 7 pages, 4 figures, 1 tabl