T
+34 946 567 842
F
+34 946 567 843
E
escalas@bcamath.org
Information of interest

A class of CTRWs: Compound fractional poisson processes
(20111231)This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. It begins with the characterization of a wellknown Lévy process: The compound Poisson process. The semiMarkov extension ...

A functional limit theorem for stochastic integrals driven by a timechanged symmetric sigmastable Levy process
(20141231)Under proper scaling and distributional assumptions, we prove the convergence in the Skorokhod space endowed with the $M_1$topology of a sequence of stochastic integrals of a deterministic function driven by a timechanged ...

A stylized model for the continuous double auction
(20121231)A stylized phenomenological model for the continuous double auction is introduced. This model is equivalent to two uncoupled M/M/1 queues. The conditions for statistical equilibrium (ergodicity) are derived. The results ...

Emerging properties of financial time series in the "game of Life"
(20111231)We explore the spatial complexity of Conway's "Game of Life," a prototypical cellular automaton by means of a geometrical procedure generating a twodimensional random walk from a bidimensional lattice with periodical ...

Ergodic transition in a simple model of the continuous double auction
(20141231)We study a phenomenological model for the continuous double auction, whose aggregate order process is equivalent to two independent M/M/1 queues. The continuous double auction defines a continuoustime random walk for trade ...

Fine structure of spectral properties for random correlation matrices: An application to financial markets
(20111231)We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded ...

Full characterization of the fractional Poisson process
(20111231)The fractional Poisson process (FPP) is a counting process with independent and identically distributed interevent times following the MittagLeffler distribution. This process is very useful in several fields of applied ...

Largescale simulations of synthetic markets
(20151008)Highfrequency trading has been experiencing an increase of interest both for practical purposes within nancial institutions and within academic research; recently, the UK Government O ce for Science reviewed the state ...

Lowtraffic limit and firstpassage times for a simple model of the continuous double auction
(201705)We consider a simplified model of the continuous double auction where prices are integers varying from 1 to $N$ with limit orders and market orders, but quantity per order limited to a single share. For this model, the ...

Modeling nonstationarities in highfrequency financial time series
(201901)We study tickbytick financial returns for the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We confirm previously detected nonstationarities. Scaling properties reported before for other highfrequency ...

On the convergence of quadratic variation for compound fractional poisson processes
(20121231)The relationship between quadratic variation for compound renewal processes and MWright functions is discussed. The convergence of quadratic variation is investigated both as a random variable (for given t) and as a ...

On the nonstationarity of financial time series: Impact on optimal portfolio selection
(20121231)We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of nonstationary behavior, and we provide empirical evidence ...

Random numbers from the tails of probability distributions using the transformation method
(20131231)The speed of many oneline transformation methods for the production of, for example, Lévy alphastable random numbers, which generalize Gaussian ones, and MittagLeffler random numbers, which generalize exponential ones, ...

Semimarkov graph dynamics
(20111231)In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semiMarkov counting process of ...

Statistical analysis and agentbased microstructure modeling of highfrequency financial trading
(20121231)A simulation of highfrequency market data is performed with the Genoa Artificial Stock Market. Heterogeneous agents trade a risky asset in exchange for cash. Agents have zero intelligence and issue random limit or market ...

Velocity and energy distributions in microcanonical ensembles of hard spheres
(20151231)In a microcanonical ensemble (constant NVE, hard reflecting walls) and in a molecular dynamics ensemble (constant NVEPG, periodic boundary conditions) with a number N of smooth elastic hard spheres in a ddimensional volume ...

Wealth distribution and the Lorenz curve: a finitary approach
(20151231)We use three stochastic games for the wealth of economic agents which may be at work in a real economy and we derive their statistical equilibrium distributions. Based on a heuristic argument, we assume that the expected ...