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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.

complexity --- cuckoo search --- magnetic resonance imaging --- fractional calculus --- musical signal --- pinning synchronization --- Fourier transform --- optimal randomness --- fractional-order system --- Mittag-Leffler function --- meaning --- parameter --- diffusion-wave equation --- anomalous diffusion --- Laplace transform --- time-varying delays --- mass absorption --- swarm-based search --- fractional --- adaptive control --- time series --- Hurst exponent --- fractional derivative --- control --- PID --- global optimization --- reaction–diffusion terms --- audio signal processing --- Caputo derivative --- harmonic impact --- fractional complex networks --- heavy-tailed distribution --- impulses --- long memory --- linear prediction

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This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

Economics, finance, business & management --- mathematical economics --- economic theory --- fractional calculus --- fractional dynamics --- long memory --- non-locality --- fractional generalization --- econometric modelling --- identification --- Phillips curve --- Mittag-Leffler function --- generalized fractional derivatives --- growth equation --- Mittag–Leffler function --- Caputo fractional derivative --- economic growth model --- least squares method --- fractional diffusion equation --- fundamental solution --- option pricing --- risk sensitivities --- portfolio hedging --- business cycle model --- stability --- time delay --- time-fractional-order --- Hopf bifurcation --- Einstein’s evolution equation --- Kolmogorov–Feller equation --- diffusion equation --- self-affine stochastic fields --- random market hypothesis --- efficient market hypothesis --- fractal market hypothesis --- financial time series analysis --- evolutionary computing --- modelling --- economic growth --- prediction --- Group of Twenty --- pseudo-phase space --- economy --- system modeling --- deep assessment --- least squares --- modeling --- GDP per capita --- LSTM --- econophysics --- continuous-time random walk (CTRW) --- Mittag–Leffler functions --- Laplace transform --- Fourier transform --- n/a --- Einstein's evolution equation --- Kolmogorov-Feller equation --- Mittag-Leffler functions

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This book is a collection of papers for the Special Issue “Quantitative Methods for Economics and Finance” of the journal Mathematics. This Special Issue reflects on the latest developments in different fields of economics and finance where mathematics plays a significant role. The book gathers 19 papers on topics such as volatility clusters and volatility dynamic, forecasting, stocks, indexes, cryptocurrencies and commodities, trade agreements, the relationship between volume and price, trading strategies, efficiency, regression, utility models, fraud prediction, or intertemporal choice.

Coins, banknotes, medals, seals (numismatics) --- academic cheating --- tax evasion --- informality --- pairs trading --- hurst exponent --- financial markets --- long memory --- co-movement --- cointegration --- risk --- delay --- decision-making process --- probability --- discount --- detection --- mean square error --- multicollinearity --- raise regression --- variance inflation factor --- derivation --- intertemporal choice --- decreasing impatience --- elasticity --- GARCH --- EGARCH --- VaR --- historical simulation approach --- peaks-over-threshold --- EVT --- student t-copula --- generalized Pareto distribution --- centered model --- noncentered model --- intercept --- essential multicollinearity --- nonessential multicollinearity --- commodity prices --- futures prices --- number of factors --- eigenvalues --- volatility cluster --- Hurst exponent --- FD4 approach --- volatility series --- probability of volatility cluster --- S&amp --- P500 --- Bitcoin --- Ethereum --- Ripple --- bitcoin --- deep learning --- deep recurrent convolutional neural networks --- forecasting --- asset pricing --- financial distress prediction --- unconstrained distributed lag model --- multiple periods --- Chinese listed companies --- cash flow management --- corporate prudential risk --- the financial accelerator --- financial distress --- induced risk aversion --- liquidity constraints --- liquidity risk --- macroeconomic propagation --- multiperiod financial management --- non-linear macroeconomic modelling --- Tobin’s q --- precautionary savings --- pharmaceutical industry --- scale economies --- profitability --- biotechnological firms --- non-parametric efficiency --- productivity --- DEA --- dispersion trading --- option arbitrage --- volatility trading --- correlation risk premium --- econometrics --- computational finance --- ensemble empirical mode decomposition (EEMD) --- autoregressive integrated moving average (ARIMA) --- support vector regression (SVR) --- genetic algorithm (GA) --- energy consumption --- cryptocurrency --- gold --- P 500 --- DCC --- copula --- copulas --- Markov Chain Monte Carlo simulation --- local optima vs. local minima --- SRA approach --- foreign direct investment --- bilateral investment treaties --- regional trade agreements --- structural gravity model --- policy uncertainty --- stock prices --- dynamically simulated autoregressive distributed lag (DYS-ARDL) --- threshold regression --- United States

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book is a collection of papers for the Special Issue “Quantitative Methods for Economics and Finance” of the journal Mathematics. This Special Issue reflects on the latest developments in different fields of economics and finance where mathematics plays a significant role. The book gathers 19 papers on topics such as volatility clusters and volatility dynamic, forecasting, stocks, indexes, cryptocurrencies and commodities, trade agreements, the relationship between volume and price, trading strategies, efficiency, regression, utility models, fraud prediction, or intertemporal choice.

academic cheating --- tax evasion --- informality --- pairs trading --- hurst exponent --- financial markets --- long memory --- co-movement --- cointegration --- risk --- delay --- decision-making process --- probability --- discount --- detection --- mean square error --- multicollinearity --- raise regression --- variance inflation factor --- derivation --- intertemporal choice --- decreasing impatience --- elasticity --- GARCH --- EGARCH --- VaR --- historical simulation approach --- peaks-over-threshold --- EVT --- student t-copula --- generalized Pareto distribution --- centered model --- noncentered model --- intercept --- essential multicollinearity --- nonessential multicollinearity --- commodity prices --- futures prices --- number of factors --- eigenvalues --- volatility cluster --- Hurst exponent --- FD4 approach --- volatility series --- probability of volatility cluster --- S&amp --- P500 --- Bitcoin --- Ethereum --- Ripple --- bitcoin --- deep learning --- deep recurrent convolutional neural networks --- forecasting --- asset pricing --- financial distress prediction --- unconstrained distributed lag model --- multiple periods --- Chinese listed companies --- cash flow management --- corporate prudential risk --- the financial accelerator --- financial distress --- induced risk aversion --- liquidity constraints --- liquidity risk --- macroeconomic propagation --- multiperiod financial management --- non-linear macroeconomic modelling --- Tobin’s q --- precautionary savings --- pharmaceutical industry --- scale economies --- profitability --- biotechnological firms --- non-parametric efficiency --- productivity --- DEA --- dispersion trading --- option arbitrage --- volatility trading --- correlation risk premium --- econometrics --- computational finance --- ensemble empirical mode decomposition (EEMD) --- autoregressive integrated moving average (ARIMA) --- support vector regression (SVR) --- genetic algorithm (GA) --- energy consumption --- cryptocurrency --- gold --- P 500 --- DCC --- copula --- copulas --- Markov Chain Monte Carlo simulation --- local optima vs. local minima --- SRA approach --- foreign direct investment --- bilateral investment treaties --- regional trade agreements --- structural gravity model --- policy uncertainty --- stock prices --- dynamically simulated autoregressive distributed lag (DYS-ARDL) --- threshold regression --- United States