research lines

Stochastic dynamics and extreme time events for socio-economic systems

Josep PerellĂł

The use of time series analysis and stochastic process modeling in complex systems studies has a long tradition, going back to to the application of Brownian (Gaussian) motion modeling to prices in the Paris stock market by Bachelier in 1900. 

These models and the statistics behind are best documented in the study of human activity patterns, and include burstiness, long-range cross-correlation and auto-correlation, and strong non-Gaussanity. We have mostly focussed on those aspects valid for the study of financial markets time series although we also recently also analyzed aspects with crutial interest in the economics of climate change.

During the last decade, the group has focused on a number of major challenges in this area including the alignment between theoretical and empirical analysis of extreme events, data driven probability inference in time-series and direct parameter estimation in agent-based modelling.

We have solved and analyzed a large class of stochastic models. Some of them are defined in terms of a Langevin equation or a stochastic differential equation and, in some cases, we also treat multidimensional and coupled diffusion processes. Another approach we have explored is by means of the so-called Continuous Time Rando Walk framework.



Relevant references

Fractional telegrapher’s equation from fractional persistent random walks

J. Masoliver
Phys. Rev E (2016)

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Quantum walk with a general coin: exact solution and asymptotic properties

Miquel Montero
QUANTUM INFORMATION PROCESSING (2015)

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Extreme values and the level-crossing problem: An application to the Feller process

Jaume Masoliver,
PHYSICAL REVIEW E (2014)

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Invariance in quantum walks with time-dependent coin operators

Miquel Montero,
PHYSICAL REVIEW A (2014)

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The Level-Crossing Problem: First-Passage, Escape and Extremes

Jaume Masoliver,
FLUCTUATION AND NOISE LETTERS (2014)

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Monotonic continuous-time random walks with drift and stochastic reset events

Miquel Montero, Javier Villarroel,
PHYSICAL REVIEW E (2013)

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Unidirectional quantum walks: Evolution and exit times

Miquel Montero,
PHYSICAL REVIEW A (2013)

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First-passage and escape problems in the Feller process

Jaume Masoliver, Josep Perello,
PHYSICAL REVIEW E (2012)

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Maximum likelihood approach for several stochastic volatility models

Jordi Camprodon, Josep Perello,
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2012)

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Scaling properties and universality of first-passage-time probabilities in financial markets

Josep Perello, Mario Gutierrez-Roig, Jaume Masoliver,
PHYSICAL REVIEW E (2011)

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Parrondo-like behavior in continuous-time random walks with memory

Miquel Montero,
PHYSICAL REVIEW E (2011)

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The impact of heterogeneous trading rules on the limit order book and order flows

Carl Chiarella, Giulia Iori, Josep Perello,
JOURNAL OF ECONOMIC DYNAMICS & CONTROL (2009)

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Perpetual American vanilla option pricing under single regime change risk: an exhaustive study

Miquel Montero,
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2009)

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