A Simple Exposition of Belief-Free Equilibria in Repeated Games

Recently, there has been made a substantial progress in the analysis of repeated games with private monitoring. This progress began with introducing a new class of sequential equilibrium strategies, called belief-free equilibria, that can be analyzed using recursive techniques. The purpose of this paper is to explain the general method of constructing belief-free equilibria, and the limit (or bound) on the set of payoff vectors that can be achieved in these strategies in a way that should be easily accessible, even for those who do not pretend to be experts in repeated games.

Building a Better Fund of Hedge Funds: A Fractal and Alpha - Stable Distribution Approach

Markowitz’s (1952) portfolio theory has permeated financial institutions over the past 50 years. Assuming that returns are normally distributed, Markowitz suggests that portfolio optimization should be performed in a mean-variance framework. With the emergence of hedge funds and their non-normally distributed returns, mean-variance portfolio optimization is no longer adequate. Here, hedge fund returns are modeled with the alpha-stable distribution and a mean-CVaR portfolio optimization is performed. Results indicate that by using the alpha- stable distribution, a more efficient fund of hedge funds portfolio can be created than would be by assuming a normal distribution. To further increase efficiency, the Hurst exponent is considered as a filtering tool and it is found that combining hedge fund strategies within a range of Hurst exponents leads to the creation of more efficient portfolios as characterized by higher risk-adjusted ratios. These findings open the door for the further study of econophysics tools in the analysis of hedge fund returns.hedge funds, fund of funds, portfolio optimization, conditional value at risk, alpha-stable distribution, Hurst exponent, fractals

A nonmanipulable test

A test is said to control for type I error if it is unlikely to reject the data-generating process. However, if it is possible to produce stochastic processes at random such that, for all possible future realizations of the data, the selected process is unlikely to be rejected, then the test is said to be manipulable. So, a manipulable test has essentially no capacity to reject a strategic expert. Many tests proposed in the existing literature, including calibration tests, control for type I error but are manipulable. We construct a test that controls for type I error and is nonmanipulable.Comment: Published in at http://dx.doi.org/10.1214/08-AOS597 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Star Formation Histories of Two Northern LMC Fields

Ground-based UBV photometry of two fields in the northern disk of the LMC are presented. A distance modulus of (m-M)_0 = 18.41 +/- 0.04 and an extinction of A_V = 0.30 +/- 0.05 has been calculated for these fields. The measurable star formation history of the LMC began no more than 12 Gyr ago with a strong star forming episode with [Fe/H] = -1.63 +/- 0.10 that accounted for approximately half (by mass) of the LMC's total star formation in the first 3 Gyr. The data does not give accurate star formation rates during intermediate ages, but there appears to have been a recent increase in the star formation rate in these fields, beginning approximately 2.5 Gyr ago, with the current metallicity in the region being [Fe/H] = -0.38 +/- 0.10. The two fields have had very similar star formation rates until 200 Myr ago, at which point one shows a large increase.Comment: 8 pages, 11 figures Accepted for publication in MNRA