Carlo Mari

Random movements of power prices in competitive markets: a hybrid model approach

This paper shows that electricity price dynamics in deregulated markets can be described by modeling the movements of the power margin level in a stochastic environment. We present a regime-switching approach to capture the main characteristics of electricity price dynamics within a supply-demand context: in the presence of stable periods, in which prices fluctuate around some long-run mean, and during turbulent periods, in which prices experience jumps and short-lived spikes of very large magnitude. The proposed approach is flexible enough to incorporate shortages in electricity generation, forced outages and peaks in electricity demand. The empirical analysis, performed to estimate the model on market data by maximum likelihood, offers an interesting agreement with the properties of observed logreturn distributions.

Mass Matrix with Symmetric Mixing and a New Parametrization of the Cabibbo-Kobayashi-Maskawa Matrix.

SummaryIn this note we propose an exponential parametrization of the Cabibbo-Kobayashi-Maskawa matrix which allows a straightforward derivation of the symmetric quark mass matrices.

Formal quantum theory of electronic rays

Abstract A quantum theory of charged beam propagation in transport magnetic structures is developed. The time coordinate of quantum mechanics is replaced by the propagation coordinate and the beam emittance takes the place of Plancks constant. Coherent beam distributions are also discussed.

Exponential parametrization of the Cabibbo-Kobayashi-Maskawa matrix and eigenstates of weak interactions

SummaryIn this note we use the exponential parametrization of the Cabibbo-Kobayashi-Maskawa matrix to obtain a simple form of the weak eigen-states recently introduced by Fritzsch and Plankl. The obtained results hold in the hypothesis of vanishingCP-violation and are obtained without the simplifying assumption of two-angle parametrization.

On the Generalized Twiss Parameters and Courant-Snyder Invariant in Classical and Quantum Optics.

SummaryIn this paper we show how the mathematical tools of the charged-beam transport theory can be applied to classical and quantum optics problems. We discuss the theory of optical-beam transport in fibers, using Twiss parameters and Courant-Snyder invariants. The same quantities are then exploited to discuss the dynamical behaviour of quantum squeezed states. Finally we present generalized Twiss parameters and Courant-Snyder invariants for quadratic Hamiltonians withn degrees of freedom.

Biunitary transformations and ordinary differential equations.—II

SummaryWe use the results of a recent reformulation of the theory of arbitrary-order differential equations in terms of non-Hermitian operators to show that the invariant binorm is associated to a generalized Courant-Snyder invariant. Furthermore, we indicate the existence of higher-order invariants associated to the Casimir operators of the group, utilized to treat higher-order equations. We also discuss the intrinsic supersymmetric nature of the theory developed. Finally, we show the relevance of the proposed mathematical technique to the design of fiberoptics transport systems.

A simplified version of the Cayley-Hamilton theorem and exponential forms of the 2 × 2 and 3 × 3 matrices

SummaryIn this note we present a simple proof of a theorem allowing us to castf(Â), where  is a non-singular matrix andf a function admitting a McLaurin expansion, as a finite sum. We also discuss the complementary version of the theorem and, limiting ourselves to 2 × 2 and 3×3 matrices, we show how they can be cast in an exponential form. Such form greatly simplifies the task of finding the π-th power (with π being any real or complex number) of a given matrix. The applications to physical problems like the optical-resonator stability and the Cabibbo-Kobayashi-Maskawa matrix are also discussed.

Linear undulator brightness: Exact analytical treatment

In this paper it is shown that the calculation of linearly polarized undulator brightness can be worked out exactly using elliptic functions and multivariable generalized Bessel functions. The obtained results are shown to be valid both in nonrelativistic and ultrarelativistic regimes. The physical relevance of the obtained results are discussed and the ‘‘low‐energy’’ corrections to the resonance condition are derived.

Risk Shaping of Optimal Electricity Portfolios in the Stochastic LCOE Theory

Abstract In this paper we review and extend the stochastic LCOE portfolio theory, a mean-risk analysis of electricity generation investment portfolios, focusing on the distinction between risk and deviation risk measures in terms of risk distribution shaping. Using standard and more advanced stochastic optimization risk measures, we derive optimal portfolios in the case of fossil fuels only, and in the case which includes the nuclear asset, interpreted as a risk free asset useful to hedge and reduce LCOE dispersion around its mean, in a US market case study. Four CO2 price volatility scenarios are used to illustrate how the theory handles the impact of indirect correlation among different fuel technologies induced by CO2 costs on the determination of optimal portfolios.

Stochastic LCOE for optimal electricity generation portfolio selection

This paper discusses a recently introduced stochastic LCOE technique for optimizing multi-asset risky energy portfolios, and extends it using an improved dynamics and CVaR as a new interesting risk measure.