Generalised relativistic Ohm's laws, extended gauge transformations and magnetic linking

Generalisations of the relativistic ideal Ohm's law are presented that include specific dynamical features of the current carrying particles in a plasma. Cases of interest for space and laboratory plasmas are identified where these generalisations allow for the definition of generalised electromagnetic fields that transform under a Lorentz boost in the same way as the real electromagnetic fields and that obey the same set of homogeneous Maxwell's equations

Multi-Lag Term Structure Models with Stochastic Risk Premia.

The purpose of this paper is to propose discrete-time term structure models where the historical dynamics of the factor (xt) is given, in the univariate case, by a Gaussian AR(p) process, and, in the multivariate case, by a Gaussian n-dimensional VAR(p) process. The factor (xt) is considered as a latent or an observable variable and, in the second case, (xt) is given by the short rate (in the scalar setting) or by a vector of several yields (in the multivariate setting). We consider an exponential-affine stochastic discount factor (SDF) with a stochastic factor risk correction coefficient defined, at time t, as an affine function of Xt = (xt, . . . , xt?p+1)0 and, consequently, the yield-to-maturity formula at time t is an affine function of the p most recent lagged values of xt+1. We study the Gaussian AR(p) and the Gaussian VAR(p) Factor-Based Term Structure Models. We investigate, under the risk-neutral and the S-forward probability, the Moving Average (or discrete-time Heath, Jarrow and Morton) representation of the yield and short-term forward rate processes. This representation gives the possibility to exactly replicate the currently-observed yield curve. We also study the problem of matching the theoretical and currently-observed market term structure by means of the Extended AR(p) approach.Discrete-time Affine Term Structure Models ; Stochastic Discount Factor, Gaussian VAR(p) processes ; Stochastic risk premia ; Moving Average or discrete-time HJM representations ; Exact Fitting of the currently-observed yield curve.

Switching VARMA Term Structure Models - Extended Version.

The purpose of the paper is to propose a global discrete-time modeling of the term structure of interest rates able to capture simultaneously the following important features : (i) an historical dynamics of the factor driving term structure shapes involving several lagged values, and switching regimes; (ii) a specification of the stochastic discount factor (SDF) with time-varying and regime dependent risk-premia; (iii) explicit or quasi explicit formulas for zero-coupon bond and interest rate derivative prices; (iv) the positivity of the yields at each maturity. The first family of models we develop is given by the Switching Autoregressive Normal (SARN) and the Switching Vector Autoregressive Normal (SVARN) Factor-Based Term Structure Models of order p. The second family of models we study is given by the Switching Autoregressive Gamma (SARG) and the Switching Vector Autoregressive Gamma (SVARG) Factor-Based Term Structure Models of order p. Regime shifts are described by a Markov chain with (historical) non-homogeneous transition probabilities.Affine Term Structure Models ; Stochastic Discount Factor ; Car processes ; Switching Regimes ; VARMA processes ; Lags ; Positivity ; Derivative Pricing.

Pricing and Inference with Mixtures of Conditionally Normal Processes.

We consider the problems of derivative pricing and inference when the stochastic discount factor has an exponential-affine form and the geometric return of the underlying asset has a dynamics characterized by a mixture of conditionally Normal processes. We consider both the static case in which the underlying process is a white noise distributed as a mixture of Gaussian distributions (including extreme risks and jump diffusions) and the dynamic case in which the underlying process is conditionally distributed as a mixture of Gaussian laws. Semi-parametric, non parametric and Switching Regime situations are also considered. In all cases, the risk-neutral processes and explicit pricing formulas are obtained.Derivative Pricing ; Stochastic Discount Factor ; Implied Volatility, Mixture of Normal Distributions ; Mixture of Conditionally Normal Processes ; Nonparametric Kernel Estimation ; Mixed-Normal GARCH Processes ; Switching Regime Models.

Nonlinear Kinetic Dynamics of Magnetized Weibel Instability

Kinetic numerical simulations of the evolution of the Weibel instability during the full nonlinear regime are presented. The formation of strong distortions in the electron distribution function resulting in formation of strong peaks in it and their influence on the resulting electrostatic waves are shown.Comment: 6 pages, 4 figure

New Information Response Functions.

We propose a new methodology for the analysis of impulse response functions in VAR or VARMA models. More precisely, we build our results on the non ambiguous notion of innovation of a stochastic process and we consider the impact of any kind of new information at a given date $t$ on the future values of the process. This methodology allows to take into account qualitative or quantitative information, either on the innovation or on the future responses, as well as informations on filters. We show, among other results, that our approach encompasses several standard methodologies found in the literature, such as the orthogonalization of shocks (Sims (1980)), the "structural" identification of shocks (Blanchard and Quah (1989)), the "generalized" impulse responses (Pesaran and Shin (1998)) or the impulse vectors (Uhlig (2005)).Impulse response functions ; innovation ; new information.

Particle acceleration and radiation friction effects in the filamentation instability of pair plasmas

The evolution of the filamentation instability produced by two counter-streaming pair plasmas is studied with particle-in-cell (PIC) simulations in both one (1D) and two (2D) spatial dimensions. Radiation friction effects on particles are taken into account. After an exponential growth of both the magnetic field and the current density, a nonlinear quasi-stationary phase sets up characterized by filaments of opposite currents. During the nonlinear stage, a strong broadening of the particle energy spectrum occurs accompanied by the formation of a peak at twice their initial energy. A simple theory of the peak formation is presented. The presence of radiative losses does not change the dynamics of the instability but affects the structure of the particle spectra.Comment: 8 pages, 8 figures, submitted to MNRA

Covariant form of the ideal magnetohydrodynamic "connection theorem" in a relativistic plasma

The magnetic connection theorem of ideal Magnetohydrodynamics by Newcomb [Newcomb W.A., Ann. Phys., 3, 347 (1958)] and its covariant formulation are rederived and reinterpreted in terms of a "time resetting" projection that accounts for the loss of simultaneity in different reference frames between spatially separated events.Comment: 3 pages- 0 figures EPL, accepted in pres

Solitary versus Shock Wave Acceleration in Laser-Plasma Interactions

The excitation of nonlinear electrostatic waves, such as shock and solitons, by ultraintense laser interaction with overdense plasmas and related ion acceleration are investigated by numerical simulations. Stability of solitons and formation of shock waves is strongly dependent on the velocity distribution of ions. Monoenergetic components in ion spectra are produced by "pulsed" reflection from solitary waves. Possible relevance to recent experiments on "shock acceleration" is discussed.Comment: 4 pages, 4 figure

Taking into account extreme events in European option pricing.

According to traditional option pricing models,1 financial markets underestimate the impact of tail risk. In this article, we put forward a European option pricing model based on a set of assumptions that ensure, inter alia, that extreme events are better taken into account. Using simulations, we compare the option prices obtained from the standard Black and Scholes model with those resulting from our model. We show that the traditional model leads to an overvaluation of at-the-money options, which are the most traded options, while the less liquid in-the-money and out-of-the-money options are undervalued.