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An attempt to obtain market directional information from non-stationary solution of the dynamic equation: "future price tends to the value maximizing the number of shares traded per unit time" is presented. A remarkable feature of the…
We prove sharp local and global variation bounds for the centred Hardy--Littlewood maximal functions of indicator functions in one dimension. We characterise maximisers, treat both the continuous and discrete settings and extend our results…
This paper considers method of creation of an advisor and indicator based on the spectral stochastic analysis model, both with linear and non-linear approximation. The problem of entrance to one or another trade position is solved on the…
This paper reviews recent developments in fundamental limits and optimal algorithms for change point analysis. We focus on minimax optimal rates in change point detection and localisation, in both parametric and nonparametric models. We…
This note proposes a method, which can be applied to searches and more in general to any cross section measurement, to maximize the analysis sensitivity.
In the study of smooth functions on manifolds, min-max theory provides a mechanism for identifying critical values of a function. In this paper we introduce a discretized version of this theory associated to a discrete Morse function on a…
The focus of this paper is on identifying the most effective selling strategy for pairs trading of stocks. In pairs trading, a long position is held in one stock while a short position is held in another. The goal is to determine the…
In this paper, we introduce a large class of (so-called) conditional indicators, on a complete probability space with respect to a sub $\sigma$-algebra. A conditional indicator is a positive mapping, which is not necessary linear, but may…
Control of drawdown, that is, the control of the drops in wealth over time from peaks to subsequent lows, is of great concern from a risk management perspective. With this motivation in mind, the focal point of this paper is to address the…
The aim of this work is to build financial crisis indicators based on spectral properties of the dynamics of market data. After choosing an optimal size for a rolling window, the historical market data in this window is seen every trading…
As a forward-looking measure of future equity market volatility, the VIX index has gained immense popularity in recent years to become a key measure of risk for market analysts and academics. We consider discrete reported intraday VIX tick…
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…
Financial markets are nonlinear with complexity, where different types of assets are traded between buyers and sellers, each having a view to maximize their Return on Investment (ROI). Forecasting market trends is a challenging task since…
Mining financial text documents and understanding the sentiments of individual investors, institutions and markets is an important and challenging problem in the literature. Current approaches to mine sentiments from financial texts largely…
Manipulation is an important issue for both developed and emerging stock markets. For the study of manipulation, it is critical to analyze investor behavior in the stock market. In this paper, an analysis of the full transaction records of…
We propose a novel symbolic modeling framework for decision-making under risk that merges interpretability with the core insights of Prospect Theory. Our approach replaces opaque utility curves and probability weighting functions with…
Characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature. This article collects a multitude of stabilizing switching signals under an…
Motivated by recent advances in the spectral theory of auto-covariance matrices, we are led to revisit a reformulation of Markowitz' mean-variance portfolio optimization approach in the time domain. In its simplest incarnation it applies to…
Given the return series for a set of instruments, a \emph{trading strategy} is a switching function that transfers wealth from one instrument to another at specified times. We present efficient algorithms for constructing (ex-post) trading…
A new approach for signal parametrization, which consists of a specific regression model incorporating a discrete hidden logistic process, is proposed. The model parameters are estimated by the maximum likelihood method performed by a…