1,093 research outputs found
Optimal Vaccination in a SIRS Epidemic Model
No full textFederico S, Ferrari G, Torrente M-L. Optimal Vaccination in a SIRS Epidemic Model. Center for Mathematical Economics Working Papers. Vol 667. Bielefeld: Center for Mathematical Economics; 2022.We propose and solve an optimal vaccination problem within a deterministic compart-mental model of SIRS type: the immunized population can become susceptible again, e.g. because of a not complete immunization power of the vaccine. A social planner thus aims at reducing the number of susceptible individuals via a vaccination campaign, while minimizing the social and economic costs related to the infectious disease. As a theoretical contribution, we provide a technical non-smooth verification theorem, guaranteeing that a semiconcave viscosity solution to the Hamilton-Jacobi-Bellman equation identifies with the minimal cost function, provided that the colosed-loop equation admits a solution. Coditions under which the closed-loop equation is well-posed are then derived by borrowing results from the theory of Regular Lagrangian Flows. From the applied point of view, we provide a numerical implementation of the model in a case study with quadrativ instantaneous costs. Amongst other conclusions, we observe that in the long-run the optimal vaccination policy is able to keep the percentage of infected to zero, at least when the natural reproduction number and the reinfection rate are small.MSC2010 subject classification: 93C15, 49K15, 49L25, 92D3
Optimal proportional and excess-of-loss reinsurance for multiple classes of insurance business
No full textIn this paper we consider a reinsurance strategy which combines a proportional and an excess-of-loss reinsurance in a risk model with multiple dependent classes of insurance business. Under the assumption that the claim number of the classes has a multivariate Poisson distribution, the aim is to maximize the expected utility of terminal wealth. In a general setting, after deriving the corresponding Hamilton–Jacobi–Bellman equation, we prove a Verification Theorem and identify sufficient conditions for the optimality. Then, in a special case with exponential utility, an explicit solution is found by solving an intricate associated static constrained optimization problem
A rescaling technique to improve numerical stability of portfolio optimization problems
No full textThis paper analyzes the numerical stability of Markowitz portfolio optimization model, by identifying and studying a source of instability, that strictly depends on the mathematical structure of the optimization problem and its constraints. As a consequence, it is shown how standard portfolio optimization models can result in an unstable model also when the covariance matrix is well conditioned and the objective function is numerically stable. This depends on the fact that the linear equality
constraints of the model very often suffer of almost collinearity and/or bad scaling. A theoretical approach is proposed that exploiting an equivalent formulation of the original optimization problem considerably reduces such structural component of instability. The effectiveness of the proposal is empirically certified through applications on real financial data when numerical optimization approaches are needed to compute the optimal portfolio. Gurobi and MATLAB’s solvers quadprog
and fmincon are compared in terms of convergence performances
Rational Normal Curves as Set-Theoretic Complete Intersections of Quadrics
No full textIn the first part of this paper we present a short survey on the problem of the representation of rational normal curves
as set-theoretic complete intersections. In the second part we use a method, introduced by Robbiano and Valla, to prove that the rational normal quartic is set-theoretically complete intersection of quadrics: it is an original proof of a classical result of Perron, and Gallarati-Rollero
Simple Varieties for Limited Precision Points
No full textGiven a finite set X of points and a tolerance epsilon representing the maximum error on the coordinates of each point, we address the problem of computing a simple polynomial f whose zero-locus Z(f) ``almost'' contains the points of X.
We propose a symbolic-numerical method that, starting from the knowledge of X and epsilon, determines a polynomial f whose degree is strictly bounded by the minimal degree of the lements of the vanishing ideal of X. Then we state the sufficient conditions for proving that Z(f) lies close to each point of X by less than epsilon. The validity of the proposed method relies on a combination of classical results of Computer Algebra and Numerical Analysis; its effectiveness is
illustrated with a number of examples
2010 Torrente de Barón
No full textAutoría:
Pablo Altamirano, Fernando Castello, Vequi Gómez
| Actúan:
Pablo Altamirano, Fernando Castello, Vequi Gómez
| Vestuario:
Alfonsina Ruiz
| Escenografía:
José Quinteros
| Operación técnica:
Maria Laura Ferreyra, Pablo Rojas
| Fotografía:
Carlos Balbastro
| Asistencia de dirección:
Maria Laura Ferreyra
| Prensa:
Daniela Bossio
| Dirección:
Paco Giménez
| Duración: 60 minutos
| Consultado el 21 de mayo de 2017
| http://www.alternativateatral.com/obra17721-torrente-de-baronAutoría:
Pablo Altamirano, Fernando Castello, Vequi Gómez
| Actúan:
Pablo Altamirano, Fernando Castello, Vequi Gómez
| Vestuario:
Alfonsina Ruiz
| Escenografía:
José Quinteros
| Operación técnica:
Maria Laura Ferreyra, Pablo Rojas
| Fotografía:
Carlos Balbastro
| Asistencia de dirección:
Maria Laura Ferreyra
| Prensa:
Daniela Bossio
| Dirección:
Paco Giménez
| Duración: 60 minutos
| Consultado el 21 de mayo de 2017
| http://www.alternativateatral.com/obra17721-torrente-de-baron
Este ítem forma parte de la colección Archivo Paco Giménez en el marco de la investigación denominada Archivo de Artistas e Intelectuales Argentinos del Centro de Estudios Avanzados de la Facultad de Ciencias Sociales de la Universidad Nacional de Córdoba
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