Carlos Ibarra Valdez

Metropolitan Autonomous University | UAM · Departamento de Matemáticas

The problem of showing the existence of cycles in the dynamics of economic systems has attracted the interest of diverse researches in the last century. The motivation relies on the fact that cycles would imply that the evolution of the economic system is intrinsically marked by non-steady growth trends, but by expansion–contraction mechanisms. Inv...

This work studies long-range correlations and informational efficiency of the Bitcoin market for the period from June 30, 2013 to June 3rd, 2017. To this end, the detrended fluctuation analysis (DFA) was implemented over sliding windows to estimate long-range correlations for price returns. It was found that the Bitcoin market exhibits periods of e...

In this paper, an adaptive extremum seeking control scheme for continuous stirred tank bioreactors is presented. Unknown growth kinetics without considering an explicit mathematical expression is assumed. An adaptive learning technique based on modeling error estimation coupled with a proportional compensation is used to construct a feedback contro...

The weak-form of the efficient market hypothesis (EMH) establishes that price returns behave as a pure random process and so their outcomes cannot be forecasted. The detrended fluctuation analysis (DFA) has been widely used to test the weak-form of the EMH by showing that time series of price returns are serially uncorrelated. In this case, the DFA...

By mid-1940s, Jackson Pollock, one of the most influential artists in the twentieth century plastic art, developed a unique painting technique (pouring and dripping) to generate complex non-figurative patterns. It has been argued that methods from fractality theory are suitable for characterizing these complex patterns. In fact, recent studies have...

The aim of this work is to obtain an equation for the effective diffusivity of permeable composite media based on an analogy with Ohm's law of electricity. Here, particles are transported across a composite medium, which is seen as an arrangement of series and parallel resistances. Comparison with simulations of Brownian particles traveling through...

This work considered the Langmuir–Hinshelwood (LH) scheme for a single reactant. In a first step, the validity of the quasi-steady state approximation (QSSA) was revised in terms of nonlinear relaxation processes. It was found that the LH equation obtained from the QSSA is not valid most of the times, except for example in the case of high reactant...

For at least one century, crude oil has been one of the most important commodities for the worldwide economic activity. Important technological innovations, including chemical transformation processes and transportation systems, have been based on the availability or not of crude oil. In this way, a close understanding of the crude oil market dynam...

The role of crude oil as the main energy source for the global economic activity has motivated the discussion about the dynamics and causes of crude oil price changes. An accurate understanding of the issue should provide important guidelines for the design of optimal policies and government budget planning. Using daily data for WTI over the period...

A critical issue for central banks in modern economies is the inflation stabilization about a prescribed level. The best-known simple instrumental rule to guide monetary policy to control inflation is the Taylor rule, where the instrument (e.g., a short interest rate) responds to changes in the inflation and the output gaps. The objective of this p...

The fractality and scaling properties of luminance patterns in Pollock's drip paintings, are studied in this paper. The painting is represented as a matrix array where each entry represents the luminance at the corresponding canva position. Detrended fluctuation analysis (DFA) is used to characterize fractality, and the results show that the whole...

A local Lipschitz condition for a dynamical stochastic coupled model of financial markets is considered. Existence and uniqueness of solu-tions and their continuous dependence with respect to the initial conditions are established. This generalization of the usual Lipschitz assumption allows to include as examples, markets with time-varying interes...

Contemporary wars make an extensive use of sophisticated weaponry and communication technologies, which allow more detailed designs of confrontation strategies. In this regard, the present paper focuses on the following questions: (i) Is contemporary war a scale-free social network? (ii) Is there any kind of memory effects in the sequence of daily...

A model coupling a deterministic dynamical system which represents trading, with a stochastic one that represents asset prices evolution is presented. Both parts of the model have connections with well established dynamic models in mathematical economics and finance. The main objective is to represent the double feedback between trading dynamics (t...

Given an excess demand function of an economy, say Z(p), a stable price adjustment mechanism (SPAM) guarantees convergence of solution path p(t,p0) to an equilibrium peq solution of Z(p)=0. Besides, all equilibrium points of Z(p) are asymptotically stable. Some SPAMs have been proposed, including Newton and transpose Jacobian methods. Despite this...

Without Abstract

An approximate formula for the Black–Scholes implied volatility is given by means of an asymptotic representation of the Black–Scholes formula. This representation is based on a variable change that reduces the number of meaningful variables from five to three. It is stated clearly which is the family of functions we are going to work, specially th...

In recent months, the crude oil market has shown an abnormal behavior as compared with the previous 20 years. The most relevant feature of it being the high-level prices, well beyond the most pessimistic forecasting of a couple of years ago. The aim of this paper is to show that the crude oil price dynamics in the period from mid-2003 to late-2004...

This paper develops a stochastic multi-model approach to describe the dynamics of crude oil prices. Based on the hypothesis that crude oil price dynamics reflects the activity of a competitive market with multiple equilibria, a mean-reversion multi-model incorporating two competitive processes with corresponding drifts and volatilities is investiga...

Some stability effects of technical trading on financial/commodity markets are analyzed in this paper. Technical trading is characterized by using past price information within a time-delay horizon to forecast future price dynamics. By introducing fundamental and technical excess demand functions, the market dynamics is modeled as a time-delayed di...

Historically, symptoms of Mexican financial crises have been strongly reflected in the dynamics of the Mexican peso to the dollar exchange currency market. Specifically, in the Mexican financial crises during 1990's, the peso suffered significant depreciation processes, which has important impacts in the macro- and micro-economical environment. In...

Markets have internal dynamics leading to stilized facts, such as fat-tails in price fluctuations and long-run memory. In this paper, we use a nonequilibrium price formation rule to explore feedback effects in trading strategies and market dynamics. By interpreting trading strategies as a feedback controller, we show that (a) trend followers can le...

A simple agent-based model is used to propose an explanation of the source of long-run memory in financial markets. It is shown that the resulting model is equivalent to a neutral-type differential equation in the price dynamics, which displays a persistence property that can be related to memory effects.

Daily records of international crude oil prices are studied using multifractal analysis methods. Rescaled range Hurst analysis provides evidence that the crude oil market is a persistent process with long-run memory effects. On the other hand, height–height correlation analysis reveals evidence of multifractal structures in the sense that the crude...

A deterministic model is introduced in terms of conservation principles to describe the (qualitative) price dynamics of a stock market. It is shown how the fundamentalist and chartist patterns of the trader behavior affect the price dynamics. The model can display complex oscillatory behavior with transient erratic oscillations, which resembles the...

In this paper, a deterministic framework for modeling stock market dynamics is presented. The model is based on assets conservation principles and consists of a series of differential equations describing the dynamics of assets trading, and a (nonlinear) functional equation describing trade conservation (i.e., what is bought (sold) by one trader is...

Blending operations are widely used in industrial plants including oil refineries, chemical plants, and cement plants. The operation mixes two or more streams with different properties to a given specification (e.g. temperatures, quality, etc.). The problem of optimal blending has been widely treated, mainly with a mathematical control theory point...

Using a simple nonequilibrium price formation model, developed in the context of agent-based trading with market orders, this paper studies the effect of learning on price dynamics. Specifically, it is shown that an agent learning on the market uncertainties (e.g., trading strategies of the other agents) can move the price dynamics towards his own...