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This book is a collection of feature articles published in Risks in 2020. They were all written by experts in their respective fields. In these articles, they all develop and present new aspects and insights that can help us to understand and cope with the different and ever-changing aspects of risks. In some of the feature articles the probabilistic risk modeling is the central focus, whereas impact and innovation, in the context of financial economics and actuarial science, is somewhat retained and left for future research. In other articles it is the other way around. Ideas and perceptions in financial markets are the driving force of the research but they do not necessarily rely on innovation in the underlying risk models. Together, they are state-of-the-art, expert-led, up-to-date contributions, demonstrating what Risks is and what Risks has to offer: articles that focus on the central aspects of insurance and financial risk management, that detail progress and paths of further development in understanding and dealing with...risks. Asking the same type of questions (which risk allocation and mitigation should be provided, and why?) creates value from three different perspectives: the normative perspective of market regulator; the existential perspective of the financial institution; the phenomenological perspective of the individual consumer or policy holder.

Medicine --- medical services’ consumption --- lifestyle factors --- insurance plan --- structural equation model --- stock–bond correlation --- VIX --- economic policy uncertainty --- monetary policy uncertainty --- fiscal policy uncertainty --- agricultural commodity futures --- price discovery --- market reflexivity --- Hawkes process --- poisson autoregressive models --- contagion --- predictive monitoring --- information-based asset pricing --- Lévy processes --- gamma processes --- variance gamma processes --- Brownian bridges --- gamma bridges --- nonlinear filtering --- house price prediction --- real estate --- machine learning --- random forest --- Lévy process --- subordination --- option pricing --- risk sensitivity --- stochastic volatility --- Greeks --- time-change --- time series --- volatility --- probability-integral transform --- ARMA model --- copula

Choose an application

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

This book is a collection of feature articles published in Risks in 2020. They were all written by experts in their respective fields. In these articles, they all develop and present new aspects and insights that can help us to understand and cope with the different and ever-changing aspects of risks. In some of the feature articles the probabilistic risk modeling is the central focus, whereas impact and innovation, in the context of financial economics and actuarial science, is somewhat retained and left for future research. In other articles it is the other way around. Ideas and perceptions in financial markets are the driving force of the research but they do not necessarily rely on innovation in the underlying risk models. Together, they are state-of-the-art, expert-led, up-to-date contributions, demonstrating what Risks is and what Risks has to offer: articles that focus on the central aspects of insurance and financial risk management, that detail progress and paths of further development in understanding and dealing with...risks. Asking the same type of questions (which risk allocation and mitigation should be provided, and why?) creates value from three different perspectives: the normative perspective of market regulator; the existential perspective of the financial institution; the phenomenological perspective of the individual consumer or policy holder.

Medicine --- medical services’ consumption --- lifestyle factors --- insurance plan --- structural equation model --- stock–bond correlation --- VIX --- economic policy uncertainty --- monetary policy uncertainty --- fiscal policy uncertainty --- agricultural commodity futures --- price discovery --- market reflexivity --- Hawkes process --- poisson autoregressive models --- contagion --- predictive monitoring --- information-based asset pricing --- Lévy processes --- gamma processes --- variance gamma processes --- Brownian bridges --- gamma bridges --- nonlinear filtering --- house price prediction --- real estate --- machine learning --- random forest --- Lévy process --- subordination --- option pricing --- risk sensitivity --- stochastic volatility --- Greeks --- time-change --- time series --- volatility --- probability-integral transform --- ARMA model --- copula

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• Reference Manager
• EndNote
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This book focuses on applications of the theory of fractional calculus in numerical analysis and various fields of physics and engineering. Inequalities involving fractional calculus operators containing the Mittag–Leffler function in their kernels are of particular interest. Special attention is given to dynamical models, magnetization, hypergeometric series, initial and boundary value problems, and fractional differential equations, among others.

Research & information: general --- Mathematics & science --- fractional derivative --- generalized Mittag-Leffler kernel (GMLK) --- Legendre polynomials --- Legendre spectral collocation method --- dynamical systems --- random time change --- inverse subordinator --- asymptotic behavior --- Mittag–Leffler function --- data fitting --- magnetization --- magnetic fluids --- Gamma function --- Psi function --- Pochhammer symbol --- hypergeometric function 2F1 --- generalized hypergeometric functions tFu --- Gauss’s summation theorem for 2F1(1) --- Kummer’s summation theorem for 2F1(−1) --- generalized Kummer’s summation theorem for 2F1(−1) --- Stirling numbers of the first kind --- Hilfer–Hadamard fractional derivative --- Riemann–Liouville fractional derivative --- Caputo fractional derivative --- fractional differential equations --- inclusions --- nonlocal boundary conditions --- existence and uniqueness --- fixed point --- gamma function --- Beta function --- Mittag-Leffler function --- Generalized Mittag-Leffler functions --- generalized hypergeometric function --- Fox–Wright function --- recurrence relations --- Riemann–Liouville fractional calculus operators --- (α, h-m)-p-convex function --- Fejér–Hadamard inequality --- extended generalized fractional integrals --- Mittag–Leffler functions --- initial value problems --- Laplace transform --- exact solution --- Chebyshev inequality --- Pólya-Szegö inequality --- fractional integral operators --- Wright function --- Srivastava’s polynomials --- fractional calculus operators --- Lavoie–Trottier integral formula --- Oberhettinger integral formula --- fractional partial differential equation --- boundary value problem --- separation of variables --- Mittag-Leffler --- Abel-Gontscharoff Green’s function --- Hermite-Hadamard inequalities --- convex function --- κ-Riemann-Liouville fractional integral --- Dirichlet averages --- B-splines --- dirichlet splines --- Riemann–Liouville fractional integrals --- hypergeometric functions of one and several variables --- generalized Mittag-Leffler type function --- Srivastava–Daoust generalized Lauricella hypergeometric function --- fractional calculus --- Hermite–Hadamard inequality --- Fox H function --- subordinator and inverse stable subordinator --- Lamperti law --- order statistic --- n/a --- Gauss's summation theorem for 2F1(1) --- Kummer's summation theorem for 2F1(−1) --- generalized Kummer's summation theorem for 2F1(−1) --- Hilfer-Hadamard fractional derivative --- Riemann-Liouville fractional derivative --- Fox-Wright function --- Riemann-Liouville fractional calculus operators --- Fejér-Hadamard inequality --- Mittag-Leffler functions --- Pólya-Szegö inequality --- Srivastava's polynomials --- Lavoie-Trottier integral formula --- Abel-Gontscharoff Green's function --- Riemann-Liouville fractional integrals --- Srivastava-Daoust generalized Lauricella hypergeometric function --- Hermite-Hadamard inequality