arXiv subjects

José Garrido

Publications and source records attributed to José Garrido.

11 recordsLinked to original sources

arXiv2026

Multiplicity distributions in DIS for heavy nucleus

We found solutions to the linear but with complicated kernel and non-homogeneous evolution equations for the cross sections of productions of $n$-cut Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomerons in the final states of high energy DIS on a nucleus, resumming all multiple rescatterings in the leading logarithmic approximation. For the model leading-twist BFKL kernel, we calculate analytical solutions of these equations by developing the homotopy approach. We also calculate the solution in the large $z=\ln\left(x_{01}^2\,Q_s^2(Y,\mathbf{b})\right)$ and large $n\gtrsim\langle n(z) \rangle$ limits, where $x_{01}$ is the dipole size, $Q_s$ the saturation scale and $\langle n(z) \rangle$ is the average multiplicity of the produced gluons. Having these cross sections we calculate the multiplicity distributions of the produced gluons and describe how the upcoming Electron-Ion Collider (EIC) can test our theoretical formalism.

hep-ph↗

arXiv2026

Comparative Analysis of Weather-Based Indexes and the Actuaries Climate Index$^{TM}$ for Crop Yield Prediction and Weather-Derivative Pricing

Climate change poses significant challenges to the agricultural and financial sectors, affecting crop productivity and overall financial stability. This study evaluates the robustness of the Actuaries Climate Index$^{TM}$ (ACI), a newer entrant in the field as a tool for measuring climate impacts, by comparing its explanatory power with well-established weather-based indexes (WBIs) across two key sectors. In the agricultural context, the yields of three major crops are predicted using generalized statistical models and advanced machine learning algorithms with climate indexes as explanatory variables. To enhance model reliability and address multicollinearity among weather-related variables, the study also incorporates both principal component analysis and functional principal component analysis. A total of 22 models, each constructed with different sets of explanatory variables, demonstrate the significant impact of wind speed and sea-level changes, alongside temperature and precipitation, on crop yield variability across six regions of the United States. For the financial market application, the analysis adapts the weather derivative framework, as it is a critical instrument for energy companies, insurers, and agribusinesses seeking to hedge against weather-related risks. By analyzing the payoffs of derivative contracts that use WBIs and ACI components as underlying variables, the findings reveal that the ACI framework holds a strong potential as a comprehensive climate risk indicator, not only for the agricultural sector but also for the finance and insurance industries.

stat.AP↗

arXiv2025

Homotopy approach for scattering amplitude for running QCD coupling

In this paper we proposed the homotopy approach for solving the nonlinear Balitsky-Kovchegov (BK) evolution equation with running QCD coupling. The approach consists of two steps. First, is the analytic solution to the nonlinear evolution equation for the simplified, leading twist kernel. Second, is the iteration procedure that allow us to calculate corrections analytically or semi-numerically. For the leading twist kernel it is shown that the first iteration leads to $\leq 1\%$ accuracy. The $ζ= -\frac{4N_c}{b_0}Y \ln\Lb \bas (1/Q^2_s(Y))/\bas\Lb r^2\Rb\Rb$ ($r$ is the dipole size, $Q_s$ is the saturation scale) and geometric scaling behaviour of the scattering amplitude are discussed as well as the dependence on the value of the infrared cutoff.

hep-ph↗

arXiv2025

Modified Homotopic approach for diffractive production

We review the recent developments of the use of the homotopy method for solving the non-linear evolution equation for the diffractive production in deep inelastic scattering. We introduce part of the non-linear corrections in the linear term. This simplified non-linear evolution equation is solved analytically taking into account the initial and boundary conditions for the process. It turns out that these corrections are rather small and can be estimated in the regular iterative procedure.

hep-ph↗

arXiv2024

Confronting impact-parameter dependent model in next-to-leading order of perturbative QCD with combined HERA data

In this talk, we present the CGC/saturation approach of Ref.[C.~Contreras, E.~Levin, R.~Meneses and M.~Sanhueza,Eur. Phys. J. C 80 (2020) no.11, 1029] and its parameters determined from the combined HERA data. This model features an analytical solution for the non-linear Balitsky-Kovchegov (BK) evolution equation and the exponential behavior of the saturation momentum on the impact parameter $b$-dependence, characterized by $Q_s\propto \exp(-mb)$. We compare our results with experimental data at small-$x$, including the proton structure function $F_2$, charm structure function $F_2^{c\bar{c}}$, and exclusive vector meson production. The model shows good agreement across a wide kinematic range. Our findings support using this approach for reliable predictions in upcoming experiments like the Electron-Ion Collider (EIC) and the LHeC.

hep-ph↗

arXiv2024

CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data

In this paper we confront the CGC/saturation approach of Ref.~\cite{CLMS} with the experimental combined HERA data and obtain its parameters. The model includes two features that are in accordance with our theoretical knowledge of deep inelastic scattering. These consist of: \textit{i}) the use of analytical solution for the non-linear Balitsky-Kovchegov (BK) evolution equation and \textit{ii}) the exponential behavior of the saturation momentum on the impact parameter $b$-dependence, characterized by $Q_s$ $\propto\exp(-mb)$ which reproduces the correct behavior of the scattering amplitude at large $b$ in accord with Froissart theorem. The model results are then compared to data at small-$x$ for the structure-function of the proton $F_{2}$, the longitudinal structure function $F_{L}$, the charm structure function $F_2^{c\bar{c}}$, the exclusive vector meson ($J/ψ,ϕ,ρ$) production and Deeply Virtual Compton Scattering (DVCS). We obtain a good agreement for the processes in a wide kinematic range of $Q^2$ at small-$x$. Our results provide a strong guide for finding an approach, based on Color Glass Condensate/saturation effective theory for high energy QCD, to make reliable predictions from first principles and for forthcoming experiments like the Electron-Ion Collider and the LHeC.

hep-ph↗

arXiv2024

Modified homotopy approach for diffractive production in the saturation region

In this paper we continue to develop the homotopy method for solving of the non linear evolution equation for the diffractive production in deep inelastic scattering(DIS). We introduce part of the nonlinear corrections as a first step of this approach. This simplified nonlinear evolution equation is solved analytically taking into account the initial and boundary conditions for the process. At the second step of our approach we demonstrated that the perturbative procedure can be used for the remaining parts of the non-linear corrections. It turns out that these corrections are small and can be estimated in the regular iterative procedure.

hep-ph↗

arXiv2023

Costate Convergence with Legendre-Lobatto Collocation for Trajectory Optimization

This paper introduces a new method of discretization that collocates both endpoints of the domain and enables the complete convergence of the costate variables associated with the Hamilton boundary-value problem. This is achieved through the inclusion of an \emph{exceptional sample} to the roots of the Legendre-Lobatto polynomial, thus promoting the associated differentiation matrix to be full-rank. We study the location of the new sample such that the differentiation matrix is the most robust to perturbations and we prove that this location is also the choice that mitigates the Runge phenomenon associated with polynomial interpolation. Two benchmark problems are successfully implemented in support of our theoretical findings. The new method is observed to converge exponentially with the number of discretization points used.

math.NA↗

arXiv2018

Bayesian Credibility for GLMs

We revisit the classical credibility results of Jewell and Bühlmann to obtain credibility premiums for a GLM using a modern Bayesian approach. Here the prior distributions can be chosen without restrictions to be conjugate to the response distribution. It can even come from out-of-sample information if the actuary prefers. Then we use the relative entropy between the "true" and the estimated models as a loss function, without restricting credibility premiums to be linear. A numerical illustration on real data shows the feasibility of the approach, now that computing power is cheap, and simulations software readily available.

stat.AP↗

arXiv2018

On Fair Reinsurance Premiums; Capital Injections in a Perturbed Risk Model

We consider a risk model where deficits after ruin are covered by a new type of reinsurance contract that provides capital injections. To allow the insurance company's survival after ruin, the reinsurer injects capital only at ruin times caused by jumps larger than a chosen retention level. Otherwise capital must be raised from the shareholders for small deficits. The problem here is to determine adequate reinsurance premiums. It seems fair to base the net reinsurance premium on the discounted expected value of any future capital injections. Inspired by the results of Huzak et al. (2004) and Ben Salah (2014) on successive ruin events, we show that an explicit formula for these reinsurance premiums exists in a setting where aggregate claims are modeled by a subordinator and a Brownian perturbation. Here ruin events are due either to Brownian oscillations or jumps and reinsurance capital injections only apply in the latter case. The results are illustrated explicitly for two specific risk models and in some numerical examples.

q-fin.RM↗

arXiv2015

Hedging of defaultable claims in a structural model using a locally risk-minimizing approach

In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Follmer-Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation Levy process and the claims pay a predetermined payout at maturity, contingent on no prior default. More precisely, in this particular framework, the locally risk-minimizing approach is carried out when the underlying process has jumps, the derivative is linked to a default event, and the probability measure is not necessarily risk-neutral.

q-fin.MF↗