The signal-noise ratio of a portfolio of p assets, its expected return divided by its risk, is couched as an estimation problem on the sphere. When the portfolio is built using noisy data, the expected value of the signal-noise ratio is bounded from above via a Cramer-Rao bound, for the case of...

In the setting of exponential investors and uncertainty governed by Brownian motions we first prove the existence of an incomplete equilibrium for a general class of models. We then introduce a tractable class of exponential-quadratic models and prove that the corresponding incomplete...

We introduce a new methodology for forecasting which we call Signal Diffusion Mapping. Our approach accommodates features of real world financial data which have been ignored historically in existing forecasting methodologies. Our method builds upon well-established and accepted methods from...

In this paper we study automatically recognized trends and investigate their statistics. To do that we introduce the notion of a wavelength for time series via cross correlation and use this wavelength to calibrate the 1-2-3 trend indicator of Maier-Paape [Automatic One Two Three, Quantitative...

The recent economic crisis has raised a wide awareness that the financial system should be considered as a complex network with financial institutions and financial dependencies respectively as nodes and links between these nodes. Systemic risk is defined as the risk of default of a large...

Many fits of Hawkes processes to financial data look rather good but most of them are not statistically significant. This raises the question of what part of market dynamics this model is able to account for exactly. We document the accuracy of such processes as one varies the time interval of...

Crashes have fascinated and baffled many canny observers of financial markets. In the strict orthodoxy of the efficient market theory, crashes must be due to sudden changes of the fundamental valuation of assets. However, detailed empirical studies suggest that large price jumps cannot be...

This paper revisits the classic gravity model in international trade and reexamines the distance coefficient. As pointed out by Frankel (1997), this coefficient measures the relative unit transportation cost between short distance and long distance rather than the absolute level of average...

In this paper we use the Brooks and Hinich cross-bicorrelation test in order to uncover nonlinear dependence periods between USA Standard and Poor 500 (SP500), used as benchmark, and six Latin American stock markets indexes: Mexico (BMV), Brazil (BOVESPA), Chile (IPSA), Colombia (COLCAP), Peru...

This paper provides the optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid" market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impacts. In addition, it is supposed that...