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Model-based and empirical analyses of stochastic fluctuations in economy and finance

Model-based and empirical analyses of stochastic fluctuations in economy and finance ArXiv ID: 2408.16010 “View on arXiv” Authors: Unknown Abstract The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis concerns statistical-based modeling and empirical analyses with applications in finance, forecasting, production processes and game theory. In these areas the time dependence of probability distributions is of prime interest and can be measured or exactly calculated for model systems. The correlation coefficients and moments are among the useful quantities to describe the dynamics and the correlations between random variables. However, the full investigation can only be achieved if the probability distribution function of the variable is known; its derivation is one of the main focuses of the present work. ...

August 14, 2024 · 2 min · Research Team

Efficient inverse $Z$-transform and Wiener-Hopf factorization

Efficient inverse $Z$-transform and Wiener-Hopf factorization ArXiv ID: 2404.19290 “View on arXiv” Authors: Unknown Abstract We suggest new closely related methods for numerical inversion of $Z$-transform and Wiener-Hopf factorization of functions on the unit circle, based on sinh-deformations of the contours of integration, corresponding changes of variables and the simplified trapezoid rule. As applications, we consider evaluation of high moments of probability distributions and construction of causal filters. Programs in Matlab running on a Mac with moderate characteristics achieves the precision E-14 in several dozen of microseconds and E-11 in several milliseconds, respectively. ...

April 30, 2024 · 1 min · Research Team