The Structure of the US Equity Markets

In 1975, Congress directed the SEC to develop a national market system in which all orders to buy or sell equities would interact. A national market system abhors fragmentation and assumes that one market will best serve the needs of all investors. Such an assumption does not capture the realities of modern markets. Investors have different needs and different markets will develop to serve these needs. Markets are non anonymous, and in such markets, the very concept of “best price” is not defined. Fragmented markets are a natural result of competition. Within the US, the sharing of trade and quote information among markets helps to mitigate any deleterious effects of fragmentation. The markets of tomorrow will be global. In a global market, the SEC will have to give up its goal of a national market system and focus on other issues. For example, it will be a challenge to provide just the sharing of trade information across borders. Further, technology will allow a market center or order-gathering function to be located anywhere in the world. This threat of relocation will place constraints on US regulators, and global trading will make it more difficult for US authorities to regulate investment practices and to protect US investors.

Optimality and Natural Selection in Markets

Evolutionary arguments are often used to justify the fundamental behavioral postulates of competive equilibrium. Economists such as Milton Friedman have argued that natural selection favors profit maximizing firms over firms engaging in other behaviors. Consequently, producer efficiency, and therefore Pareto efficiency, are justified on evolutionary grounds. We examine these claims in an evolutionary general equilibrium model. If the economic environment were held constant, profitable firms would grow and unprofitable firms would shrink. In the general equilibrium model, prices change as factor demands and output supply evolves. Without capital markets, when firms can grow only through retained earnings, our model verifies Friedman's claim that natural selection favors profit maximization. But we show through examples that this does not imply that equilibrium allocations converge over time to efficient allocations. Consequently, Koopmans critique of Friedman is correct. When capital markets are added, and firms grow by attracting investment, Friedman's claim may fail. In either model the long-run outcomes of evolutionary market models are not well described by conventional General Equilibrium analysis with profit maximizing firms.evolution, natural selection, equilibrium, incomplete markets

Lexiocographic Refinements of Nash Equilibrium

The fundamental idea of game theory is that each player in the game acts in his own best interests, given the actions of the other players. Nash equilibrium makes this idea precise by defining each player's best interests as the maximization of his expected utility, where the expectation is taken with respect to the (mixed) strategies played by the other players. New equilibrium concepts and refinements of old equilibrium concepts should adhere to this fundamental idea of self-interested action. This is to say, they must be justified in decision-theoretic terms. A notion of "self-interest" must be defined by specifying the preferences of the players, and equilibrium must be defined with respect to these preferences. This paper characterizes preferences that justify perfect and proper equilibrium as the outcome of rational, self-interested behavior.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100637/1/ECON113.pd

Development of UHF radiometer

A wideband multifrequency UHF radiometer was initially developed to operate in the 500 to 710 MHz frequency range for the remote measurement of ocean water salinity. However, radio-frequency interference required a reconfiguration to operate in the single-frequency radio astronomy band of 608 to 614 MHz. Details of the radiometer development and testing are described. Flight testing over variable terrain provided a performance comparison of the UHF radiometer with an L-band radiometer for remote sensing of geophysical parameters. Although theoretically more sensitive, the UHF radiometer was found to be less desirable in practice than the L-band radiometer

Effective renormalized multi-body interactions of harmonically confined ultracold neutral bosons

We calculate the renormalized effective 2-, 3-, and 4-body interactions for N neutral ultracold bosons in the ground state of an isotropic harmonic trap, assuming 2-body interactions modeled with the combination of a zero-range and energy-dependent pseudopotential. We work to third-order in the scattering length a defined at zero collision energy, which is necessary to obtain both the leading-order effective 4-body interaction and consistently include finite-range corrections for realistic 2-body interactions. The leading-order, effective 3- and 4-body interaction energies are U3 = -(0.85576...)(a/l)^2 + 2.7921(1)(a/l)^3 + O[(a/l)^4] and U4 = +(2.43317...)(a/l)^3 + O[(a\l)^4], where w and l are the harmonic oscillator frequency and length, respectively, and energies are in units of hbar*w. The one-standard deviation error 0.0001 for the third-order coefficient in U3 is due to numerical uncertainty in estimating a slowly converging sum; the other two coefficients are either analytically or numerically exact. The effective 3- and 4-body interactions can play an important role in the dynamics of tightly confined and strongly correlated systems. We also performed numerical simulations for a finite-range boson-boson potential, and it was comparison to the zero-range predictions which revealed that finite-range effects must be taken into account for a realistic third-order treatment. In particular, we show that the energy-dependent pseudopotential accurately captures, through third order, the finite-range physics, and in combination with the multi-body effective interactions gives excellent agreement with the numerical simulations, validating our theoretical analysis and predictions.Comment: Updated introduction, correction of a few typos and sign error

Quantum Monte Carlo study of quasi-one-dimensional Bose gases

We study the behavior of quasi-one-dimensional (quasi-1d) Bose gases by Monte Carlo techniques, i.e., by the variational Monte Carlo, the diffusion Monte Carlo, and the fixed-node diffusion Monte Carlo technique. Our calculations confirm and extend our results of an earlier study [Astrakharchik et al., cond-mat/0308585]. We find that a quasi-1d Bose gas i) is well described by a 1d model Hamiltonian with contact interactions and renormalized coupling constant; ii) reaches the Tonks-Girardeau regime for a critical value of the 3d scattering length a_3d; iii) enters a unitary regime for |a_3d| -> infinity, where the properties of the gas are independent of a_3d and are similar to those of a 1d gas of hard-rods; and iv) becomes unstable against cluster formation for a critical value of the 1d gas parameter. The accuracy and implications of our results are discussed in detail.Comment: 15 pages, 9 figure