Henryk Gzyl Buchholz

Profesor visitante del Centro de Finanzas IESA

Áreas de Interés

Teoría de Probabilidades y sus Aplicaciones en Ecuaciones Diferenciales y en Matemáticas Financieras, Problemas Inversos, Modelos Matemáticos, Matemáticas Financieras.

  • Ph.D. en Matemáticas, University of California (San Diego, EE.UU.)
  • Licenciado en Física, Universidad Central de Venezuela (Caracas, Venezuela)

Amplio espectro de cursos dictados en las licenciaturas y en los postgrados en Física, en Matemáticas y Finanzas en las varias instituciones.

  • 2010: Catedrático Invitado, Departamento de Estadística, Universidad Carlos III de Madrid (España)
  • 2007 - presente: Profesor Invitado del Centro de Finanzas del Instituto de Estudios Superiores de Administración (IESA)
  • 2007 – 2010: Profesor Invitado, Depto. de Métodos Cuantitativos, Facultad de Economía, Universidad de Navarra
  • 2005 - 2007: Profesor Titular en el Departamento de Cómputo y Estadística de la Universidad Simón Bolívar (USB)
  • 2004 - 2005: Catedrático Invitado, Departamento de Estadística, Universidad Carlos III de Madrid (España)
  • 1998 - 2004: Profesor Titular en el Departamento de Cómputo y Estadística de la Universidad Simón Bolívar (USB)
  • 1983 - presente: Profesor Titular de la Escuela de Física y Matemáticas, Facultad de Ciencias, Universidad Central de Venezuela (UCV)

Arbitro ocasional para:

  • Acta Científica Venezolana
  • American Statistician
  • Comm. in Stochastics
  • Hadronic Journal
  • Journal of Operational Risk
  • Journal of Transport Theory and Stat
  • Mathem. of Oper. Research
  • Methodology and Computing in Applied Probability
  • Physica A
  • Physical Review A
  • Physics
  • Quantitaive Finance

 

Reseñista ocasional de libros para:

  • Acta Applic. Mathematicae
  • Mathematical Revs.
  • Zentralblatt f. Mathematik

Publicaciones científicas

  • “Interpretación combinatoria de polinomios de tipo binomial”. Acta Cient. Venez. 27, pp. 244-246 (1976).
  • “Levy systems for time changed processes”. Annals of Probability, 5, pp. 565-570 (1977).
  • “Poblaciones en medios aleatorios: modelos simples”. Acta Cient.Venez. 26, 224-225.
  • “On entrance-exit distributions of Markov processes” (con C. Betz) Jour. App. Prob. 15, pp. 78-86 (1978).
  • “On generators of subordinate semigroups”. Annals of Probab., 6, No. 6, 975 - 983. (1978),
  • “Occupation time sets of supports of continuous additive functionals”, (con C. Betz). Annals
  • Inst. Henri Poincaré, 15, No.1, p. 41 -50, (1979)
  • “Quantum systems subject to random pulses”, Jour. Math. Phys. 18, pp. 1327-l329 (1980).
  • “Infinitesimal generators of time changed processes”. Annals of Probability, 8, No.4 p p.716-726 (1980).
  • ”Some relations between exit measures hitting measures and Levy systems for standard processes”. Acta Cient.Venez, 30, No. 2, pp. 328-330 (1979)
  • ”A unified presentation of equilibrium distributions in classical and quantum mechanics”. Annals Inst Henri Poincaré, 32, pp. 175-183 (1980).
  • “On the probabilistic solution of a non-Homogeneous Cauchy Boundary Value Problem”. Acta Cient. Venez., 30, pp. 440-4451980.
  • “0n Blume’s integration of Schroedinger’s equations for a quantum system subject to Random Pulses”, Jour. Math. Phys., 20 No. 8, pp. 1174-1175 (1979).
  • “A necessary condition for the existence of global solutions dXt = a (Xt) dBt” (con C. Betz). Jour. Stoch. Proc. 11, pp. 313-31 5 (1981).
  • “On the equivalence of some exact master equations”. Jour. Stat. Phys. 26 No.4 (1981).
  • “On an abstract averaging theorem”. Acta Cient. Venez. 32, pp. 282-283 (1981).
  • “Integration of the Boltzman equation in the relaxation time approximation”, Journ. Stat. Phys. 29, pp. 617-622 (1982).
  • “Linearized Boltzman equations 1: Representation of solutions”. Jour. Stat.Phys. 28 (1982) 165-171.
  • “Quantization on the damped harmonic oscillator”. Phys. Rev. A.27 No.5 2297-2299 (1983).
  • “Bounds for the first eigenvalue of a spherical cap”. (w.C. Betz and G. Camera). Appl. Math. And Optimizat. 10, pp. 193-202 (1983).
  • “Quantum mechanical solution of the linear filtering problem”. Letters in Systems and Control. 3, pp. 217-220 (1983).
  • “On the computation of conditional probabilities”. Acta Cient. Venz. 35, pp. 79-80 (1984).
  • Evolution semigroups and hamiltonian flows”. Jour. Math. Analysis and Applic. 110, pp. 316-332 (1985).
  • ’‘Canonical transformations, umbral calculus and orthogonal theory”. Jour. Math. Analysis and Applications. 111, pp. 547-558 (1985).
  • “Integrable systems, their associated (semi) groups and moment systems”. Jour. Math. Analysis and Applications, 115, pp. 506-516 (1986).
  • “A simple proof of Faa di Bruno’s Formula”. Acta Cient. Venez. 37, No.2, pp. 214-21 5 (1986).
  • “Multidimensional extension of Faa di Bruno’s formula and applications”. Jour. Math, Analysis and Applications. 116, pp. 450-455 (1986).
  • “Probabilistic methods for comparing first eigenvalues’‘ (con C. Betz) Ann. Inst. Henri Poinceré, Vol. 21 No. 2 (1985) pp. 147-156.
  • “Bounded vs. Free”. Hadronic Jour., 8, No.2, pp. 119-120 (1985).
  • “Perturbative and asymptotic expansions of exact memoryless master equations” (con L. Kababe). Acta. Phys. Polonica, A691, pp. 167-177 (1986).
  • “Non-unitary representations of canonical transformations and application to filtering theory”, Vol. Conmemorativo de Acta Cient´ıfica Venezolana, 30, pp. 620-624 (1987).
  • “On the equivalence of Hamiltonians leading to Newtonian equations” (con L. A. Herrera). Hadronic Journal, 9, pp. 31-34 (1986).
  • “On the integration of the Heisenberg equations of motion”. Hadronic Journal. 9, No.4, pp. 171-172 (1986).
  • “Umbral calculus via integral transforms”, Jour. Math. Analysis and Appl. 129 No.2, pp. 315325 (1988).
  • “Kinetic equation for Ising model in a convolutionless formalism”, (con L. Kabbabe). Acta Physica Polonica. A72, pp. 721-727 (1987).
  • “Removing ambiguities in some classical and quantum descriptions of a particle in a magnetic field”. Hadronic Journal. Vol 9, 177-179.
  • “Characterisation of vector valued, Gaussian, stationary Markov processes”. Lettters in Probability and Statistics. 6, pp. 17-19 (1987).
  • “Diffusions on some submanifolds of euclidean spaces”. Letters in Prob. and Statistics. 10, pp. 311-315 (1990).
  • “The Feynman-Kac formula and Hamilton-Jacobi equation”. Jour. Math. Analysis and its Applications, 142, pp. 79-82 (1989).
  • “On the physicists approach to the travelling salesman problem”, (con R. Jiménez) Mathl. And Comp. Mod. 12 pp. 667-670 (1989).
  • “Classical limits via brownian motion” Appeared in Commemorative Vol.100 of Fac. Ciencias U.L.A. (con J.R. León) (1989) pp. 83-90.
  • ’‘Linear programming with maximumentropy”, Mathl. and Computer Modeling. (con F. Gamboa). 13, pp. 49-52 (1990)
  • “Probabilistic representation of solutions of wave equations”. (con R. Jim6nez) Math. and Computer Modelling, 13 p. 57-65 (1990).
  • “On the physicists approach to the travelling salesman problem II”. Mathl. and Comp. Modelling (con R Jiménez. and A. Quiroz) 13, pp. 45-48 (1989). 44 “The maxent approach to linear programming with quadratic errors”Mathl. and Computer Modelling. 15, pp. 43-45 (1990).
  • “Probabilistic representation of solutions of wave equations. II: Boundary value problems”. Mathl. and Computer Modelling. 13 pp. 67-76 (1990).
  • “Probabilistic approach to wave propagation problems III: Brownian local times and waves in layered media”, Mathl. and Comp. Modelling. 15, pp. 65-62 (1991).
  • “Probabilistic methods for waves in heterogeneous media”, IUTAM Symp. In Linear and nonlinear waves. Bellomo, N. and Casciatti, F. (eds). Springer-Verlag, (1992), pp. 266-272.
  • “Diffusions and Waves”, (con R Jiménez) Jour. Math. Analysis and Appl., 174, pp. 498-517 (1993)
  • “Probabilistic representation of solutions of wave equations IV: Reflecting boundaries”. Mathl. and Comp. Mod. (con C. Betz) 15, pp. 129.140 (1991).
  • “From the heath to the wave equations” (w. R. Jiménez) Math. and Comp. Modelling, 16, pp. 69-71 (1992).
  • “Probabilistic representation of solutions to wave equations V: a collection of examples”. Mathl and Computer Modelling. (con C. Betz and R. Jiménez)16, pp. 165-176 (1992).
  • “A path integral approach for solving Euler’s equation describing the oscillations of an infinite bar”. Mathl. and Comp. Modelling, 19, 119-124 (1994)
  • “Hitting distributions and the Sommerfeld radiation condition”, (con C. Betz) Jour. Math. Analysis and Appl., 182 pp. 301-308 (1994).
  • “Hitting Spheres from the exterior” (w. C. Betz), Ann. Of Probab. 22, pp. 177-179 (1994)
  • “Paradigmas Predictivos: predicción en régimen caótico”, Interciencia, Vol. 20, p37-39, 1995.
  • “Maxentropic reconstruction of Fourier and Laplace transforms”, Appl. Math and Comp., Vol. 73, pp. 181-189 (1995).
  • “Maxentropic reconstruction of Fourier and Laplace Transforms under non-linear constraints”, Appl. Math and Comp. Vol. 25 (1997), pp. 117-126.
  • “On a maxentropic procedure for reconstructing a distribution from its marginals” (with .B. Herrero) Mathl. and Comp. Modelling. Vol. 24 (1996), pp. 83-89.
  • “Maxentropic solutions of linear Fredholm equations” (con F. Gamboa). Mathl. & Comp. Modelling, Vol. 25, pp. 23-32 (1997).
  • “Maxentropic analysis of of linear programming problems”. (con F. Moreno) Mathl. & Computer Modelling. Vol.26 (1997) pp. 107-116.
  • “The Weierstrass approximation theorem and large deviations”, (con J.L Palacios) Amer. Mathem. Montlhy. Vol.104 (1997, pp. 656-659.
  • “Parameter estimation in superpositions of decaying exponentials” (con C. Chang) Appl.Math. & Computation, Vol.96 (1998) pp. 101-116.
  • “Maxentropic reconstructions in the presence of noise”. in Maximum Entropy and Bayesian Methods, Vol. 17, Erickson, G. and Ryckert, J. (eds), Kluver Pubs, (1998).
  • “Maxentropic reconstruction with uncertainty in the data and varying a priory infor- mation”, (con. Y. Velásquez) Mathem. and Computer Modelling, Vol. 29 (1999) pp. 79-86.
  • “A comparative study of some reconstruction methods for linear inverse problems” (con A. Tagliani y Y. Velásquez), Computer and Mathem. Modeling, Vol 30 (1999) pp. 159-167
  • “The role of a priori information in maxentropic reconstruction in the mean”, (con Y. Velásquez). Applied Math. and Comput. Vol. 109 (2000) pp. 101-119.
  • Gzyl, H. “Linear reconstruction problems with convex constraints: influence of the a priori data” (con Y. Velásquez). Applied Mathematics and Computation. Vol. 109, pp. 189-198.
  • “Maxentropic characterization of some probability distributions”, Studies in Applied Math. Vol 105 (2000) pp235-243.
  • “Probabilistic remarks in the theory of scattering by soft obstacles”, Studies in Applied Math. Vol.105 (2000), 375-384.
  • “Maxentropic construction of risk neutral measures”, Applied Math. Finance. Vol 7 (2000) pp. 229-239.
  • Maxentropic reconstruction by first order splines” (con Y. Velásquez) Maximum Entropy and Bayesian Methods, J.Ryckert, Erickson, G. and Smith, G. (eds), AIP- CP 547, Amer. Inst. of Phys., (2001) pp. 181-196.
  • ”Inverse problems for the acoustic wave equation: a probabilistic approach to uniqueness and approximation”. Applied Math. and Comput. Vol. 122 (2001) pp. 179-194.
  • “Maxentropic interpolation by cubic splines with possibly noisy data”, (con Y. Velásquez) in Maximum Entropy and Bayesian Methods, A. Mohammad-Djafari (ed.), AIP-CP568, 2001, 216-228.
  • “A generalized maxentropic inversion procedure for noisy data”, (with A. Golan) Applied Math. and Computation, Vol. 127 (2002) pp. 249-260.
  • “Tomographic reconstructions by maximum entropy”, Appl. Math. and Computation. Vol. 129 (2002) 157-169.
  • “Reconstruction of transition probabilities by maximum entropy in the mean”, (con. Yurayh Velásquez) Maximum Entropy and Bayesian Methods, AIP CP Vol.617 (2002), 192-203.
  • “Maxentropic determination of minimum energy states from partial observation”, (con M. Diasparra) Maximum Entropy and Bayesian Methods, AIP- CP Vol.617 (2002), 322-330
  • “On Poisson-Dirichlet problems with polynomial data”, Publications Matemátiques., Vol. 46  (2002), 465-471.
  • “Entropic approach to interior point solution of linear programs”, (con. M.Diasparra) Appl. Math. and Comp., Vol. 143 (2003), 339-347.
  • “Ill-posed linear inverse problems and maximum entropy in the mean”, Acta Cient´ıfica Ven. Vol. 53 (2002) 71-90.
  • “Probabilistic approach to an image reconstruction problem”, (w. Noam Zeev) Methodology and Comp. in Appl. Probab. 4 (2002) 307-318.
  • “A perturbative approach for reconstructing diffusion coefficients”, (w. M. Villasana) Appl. Math. and Computation (2004)
  • “Priors and Information-Theoretic Estimation”, (with Amos Golan) Proceedings of the American Statistical Association Business and Economic Section, IEE Conference (2003)
  • “On the approximation properties of Bernstein polynomials via probabilistic tools”, (w. J.L. Palacios) Bol. Asoc. Matem. Venezolana. Vol.X, (2003) pp. 5-13.
  • “Maximum Entropy in the Mean: A useful tool for constrained linear problems”, (A tutorial) Bayesian Inference and Maximum Entropy, Am. Inst. Phys., CP 695, (2003) pp. 361-385
  • “Geometry and exponential coordinates for probabilities on a finite set“. Bayesian Inference and Maximum Entropy, Am. Inst. Phys., CP 375 (2004) pp. 481-492.
  • “Maxentropic solution of fractional moment problems”, (with Inverardi, Tagliani y Villasana) 173 (2006) pp. 109-125.
  • “Classical analogues of quantum paradoxes”, Boletin de la AMV, 2004.
  • “Geometry on the space of probabilities I: the finite dimensional case”, (with L. Recht) Revista Matemática Iberoamericana. 22, pp (2006) pp. 545-558.
  • “Geometry on the space of probabilities II: projective spaces and exponential families”, (with L. Recht) Revista Matemática Iberoamericana. Vol 3 (2006), 833-849.
  • “An exposé on discrete Wiener chaos expansions” Boletin de la AMV, XIII, No 1, (2006) pp. 3-25.
  • “A new bound on discrete distributions based on maximum entropy” AIP. CP. 872, pp. 425-432 (2006)
  • “Intrinsic geometry on the class of probability densities and exponential families” (with L. Recht) Publications Matematiques., Vol. 51 (2007) 309-332.
  • “In search of the best approximant” (con P.L Novi-Inverardi y Aldo Tagliani) Appplied Mathematics and Computation, Vol. 189 (2007), pp. 652-661.
  • “On a relationship between distorted and spectral risk measures” (con Silvia Mayoral) Revista de Econom´ıa Financiera, 15 (2008), pp. 8-21.
  • “Geometry on the space of positive functions” (with Lazaro Recht) Boletin de la Asociación Matemática Venezolana, XIV (2007) pp 15-26.
  • “Determination of risk measures from market prices of risk”, (with Silvia Mayoral) Insurance: Mathematics and Economics, 43 (2008) 437-443.
  • “Determination of the joint probability distribution of a family of binary random variables. Applications to risk measurement”, (con Aldo Tagliani) The Wilmott Magazine, July (2008) pp 64-69.
  • “Bayesian Parameter Inference for Assets in models of the Black & Scholes type” (con Enrique ter Horst and Samuel Malone) Applied Stochastic Models in Business and Industry, Volume 24 Issue 6, November 2008
  • “Recovering decay rates from noisy measurements with maximum entropy in the mean” (con Enrique ter Horst) Journal of Probability and Statistics, 2009 (2009), pp. 1-13
  • “A proposal for a new bound for discrete distributions” (con P.L Novi-Inverardi y Aldo Tagliani) Communications in Satistics: Theory and Methods. 37 (2008) pp. 2149 - 2161
  • “Inverse problems for random walks on trees: network tomography” (with Victor de la Peña y Patrick McDonald) Statistics and Probability Letters 78 (2008), 3176-3183.
  • “Assessment and Propagation of Input Uncertainty in Tree-based Option Pricing Models” (with Germán Molina and Enrique ter Host) Applied Stochastic Models in Business and Industry, Volume 25 Issue 3, May 2009
  • “Hitting time and inverse problems for Markov chains” (with Victor de la Pe˜na y Patric Mc Donald) Journal of Applied Probability, 45 (2008) pp 640-649.
  • “A method for determining risk aversion functions from uncertain market prices of risk” with Silvia Mayoral Insurance: Mathematics and Economics, 47 (2010), 84-89
  • “Stieltjes moment problem and fractional moments” (con Aldo Tagliani) Applied Mathematics and Computation, 216 (11), (2010) 3307-318.
  • “A concentrated non-linear information theoretic estimator for the sample selection model”  (con Amos Golan) Entropy 2010, 12 (6), 1569-1580; doi: 10.3390/e12061569
  • “Stochastic volatility models including open, close, high and low prices” (con E. ter Horst, G. Molina y A. Rodr´ıguez) Quantitative Finance, 12, Issue 2, 2012, 199-212
  • “Hausdorf moment problem and fractional moments” (Con Aldo Tagliani) Applied Mathematics and Computation, 216, Issue 11, pp. 3319-3328
  • “Determination the distribution of total loss from the moments of its exponential” The Journal of Operational Risk, 2011, 6/Number 3, 3-13.
  • “Determination of the probability distribution measures form market option prices using the method of maximum entropy in the mean” (Con Silvia Mayoral) Applied Mathematical Finance, 19, 299-312 (2012)
  • “Computing the value-at- risk of aggregate severities” Journal of Operational Risk, 6/Number 4 (2011), 1-5.
  • “An entropic linear estimator for inverse problems” (con Amos Golan) Entropy, 14, (2012), pp. 892-923.
  • “Reconstructing heavy-tailed distributions by splicing with maximum entropy in the mean”  (con Santiago Carrillo y Aldo Tagliani) Journal of Operational Risk, 7 (2) (2012) pp. 1-13.
  • ”Determination of the total loss from the fractional moments of its exponential” (Con Aldo Tagliani y Pier L Novi.) Applied Mathematics and Computation 219, (4), 1 (2012) pp. 2124-2133
  • “A comparison of numerical approaches to determine severity of losses” (Con Aldo Tagliani y Pier L Novi.) Jour. of Operational Risk, 8 (1) (2013) pp. 3-15.
  • ”On a further extension of Osuna’s model for psychological stress” (con E.E Osuna). Jour. Contem. Mathem. Sciences, 8 (2013) pp. 801-814.
  • “The Laplace transform on the real line is truly ill conditioned” (con Aldo Tagliani), Applied Mathematics and Computation. 219 (2013) 9805-9809.
  • “Determination of the probability of ultimate ruin by maximum entropy applied to fractional moments” (Con Aldo Tagliani) Insurance: Mathematics and Economics, 53 (2013) pp. 457-463.
  • ”Fractional Moments and Maximum Entropy: Geometric Meaning” (Con Aldo Taliani y Pier L. Novi) Communications in Statistics, 43, (2014), 3596-3601.
  • “A relationship between the ordinary maximum entropy method and the method of máximum entropy in the mean” (con Enrique ter Horst) Entropy 16 (2014) pp. 1123-1133.
  • “Disentangling frequency models” (con Erika Gómes) Journal of Operational Risk (2014), 9, 1-18.
  • “Numerical determination of hitting time distributions from their Laplace transforms: Simple cases” (con Enrique ter Horst) Physica A (2014), 410, 244-262.
  • “Density reconstructions with errors in the data” (con Erika Gomes y Silvia Mayoral), Entropy 2014.
  • Numerical determination of hitting time distributions: from their Laplace transforms: One dimensional diffusions” (con Enrique ter Horst y Minaya Villasana) Physica A (2015), 419, 594-402.
  • “Evaluación ecocardiográfica de la contribución auricular durante la estimulación ventricular II. Análisis de la proporción de ciclos cardíacos con contribución auricular”. (con R. Curiel, J. Octavio y J. Pérez-González) Rev. Espa˜nola de Cardiolog´ıa. (1984) 37, 257-260.
  • “Two maxentropic approaches to determine the probability density of compound risk losses”  (con Erika Gomes y Silvia Mayoral) Insurance: Mathematics and Economics, (2015) 62, 42-53.
  • “A spectral measure estimation problem in rheology”, (con E. ter Horst y Germán Molina), Physica A, (2015), 434, 129-133.
  • “Entropy and density approximation from Laplace transforms” (con A. Tagliani y P.L. Novi-Inverardi) Applied Mathematics and Computation (2015), 265, 225-236.
  • “Maxentropic approach to decompound aggregate risk losses” (con E. Gomes y S. Mayoral) Insurance: Mathematics and Economics (2015), 64, 326-336.
  • “Maximum entropy approach to the loss data aggregation problem” (con E. Gomes y S. Mayoral),  Journal of Operational Risk, (2016), 11, 49-70.
  • “Determination of zero-coupon and spot rates from treasury data by maximum entropy methods (con S. Mayoral). Physica A (2016). 456, 36-50.
  • “Recovering a distribution from its translated fractional moments” (con Aldo Tagliani) Statistics and Probability Letters (2016), 118, 171-176.
  • ”Loss data analysis: Analysis of the sample dependence in density reconstruction by maxentropic methods” (con Erika Gomes y Silvia Mayoral), Insurance: Mathematics and economics, (2016),  71, 154-153
  • “Is it better to predict by minimizing squared distance or by minimizing variance?” (Teaching Note) Boletin Asoc. Matem. Venezolana. (2016), XXIII, 81-84
  • “Sample dependence in the maximum entropy solution to the generalized moment problem” Journal of Probability and Statistics (2016) https://doi.org/10.1155/2016/8629049.
  • “Discontinuous payoff option pricing by Mellin transform: a probabilistic approach”. (Con M. Milev y A. Tagliani), Financial Research Letters. (2016)
  • “Superresolution in the maximum entropy approach to invert Laplace transforms” Inverse problems in Science and Engineering, 25, 1536-1545 (2017).
  • “Maxentropic solutions to a convex interpolation problem motivated by utility theory” (con Silvia Mayoral), Entropy, 19, 153, (2017).
  • “Inferring probability densities from expert opinion” (con E. ter Horst y G. Molina) Applied Mathematical Modeling, (2017), 43, 306-320.
  • “Calibration of short rate term structure models from bid-ask coupon bond prices, (con Erica  Gómes-Goncalves y Silvia Mayoral), Physica A, (2018), 492, 1456-1472
  • “Modeling Large Losses” Journal of Operational Risk. (2018)
  • “Loss data analysis with maximum entropy”, Mathematical and Statistical Methods for Actuarial Sciences and Finance, (2018) Springer.
  • “Risk neutral measure determination from price ranges: Single period market models” (con ter Horst, E y Molina, G.) Entropy 2018, 20 (7), https://doi.org/10.3390/e20070508.
  • “Maximum Entropy in the Mean Methods in Propensity Score Matching for Interval and Noisy Data” (with Gunn, L., ter Horst, E y Molina, G.). Communic. in Statistics, Series B. (2018)
  • “A Model-Free, non-Parametric Method for Density Determination, with Application to Asset Returns” (con Enrique ter Horst y Germán Molina). . Physica A. (2018)
  • “Sample dependence of risk premia”, (with E. Gomes-Con¸calves y S. Mayoral). Jour. Operational Risk
  • “Geometry and Fixed-Rate Quantization in Riemannian Metric Spaces Induced by Separable Bregman Divergences” (con Erika Gomes y Frank Nielsen) Cap´ıtulo en “Geometry of Information”, Springer Nature, (2019).
  • “Best predictors in logarithmic distance between positive random variables”, Jour. Appl. Math., Stat. and Information, (2019), 15, 15-28.
  • “A review of maximum entropy methods for loss data aggregation and disaggregation problems”,  (with E. Gomes-Con¸calves y S. Mayoral) Entropy, 2019.
  • “Hitting spheres with brownian motion revistited” Statistics and Probability Letters 155, (2019) https://doi.org/10.1016/j.spl.2019.108565
  • “The Hamilton-Jacobi equation, the Feynman-Kac formula and the Classical Limit”, Publ. Unión Matemát. Uruguay, 17, 81-92.
  • “Construction of contingency tables by maximum entropy in the mean”, Communications in Statistics: Theory and Methods, (2020) https://doi.org/10.1080/03610926.2020.1723639.
  • “Portfolio optimization in incomplete markets and price constraints determined by máximum entropy in the mean”, (Con A. Arratia) Computational Economics, (2019) https://doi.org/10.1007/s10614-019-09954-3.
  • “Prediction in Riemannian metrics derived from divergence functions”, Communications in Statistics, (2020), https://doi.org/10.1080/03610926.2020.1752384
  • “Geometry of the probability simplex and its connection to the maximum entropy method” (with Frank Nielsen), Jour. Appl. Math., Stat. and Information (May 2020).
  • “Extracting Pricing Densities for Weather Derivatives Pricing using the Maximum Entropy Method”, Journal of the Operational Research Society, (con Alexandridis, A., ter Horst, E y Molina, G.), https://doi.org/10.1080/01605682.2020.1796532
  • “A constrained ill-posed linear problem with data in intervals arising in geodetic leveling”, Bull. Comput. & Appl. Mathem., 8, (2020). (con Mayoral, S.)
  • “Electrical power diversification: An approach based on the method of maximum entropy in the mean” (con R. Bautista, E. ter Horst, y G. Molina) Entropy (2021). Open access. https://www.mdpi.com/1099-4300/23/3/281
  • “Harmonic Oscillators, Waves and Gaussian Processes” . Statistics and Probability Letters,  (2021) https://doi.org/10.1016/j.spl.2021.109043.
  • “Diversification can control probability of default or risk, but not both” (con Pedro Cadenas) Journal of Financial Risk Management (2021). Open access https://www.mdpi.com/1911-8074/14/2/73
  • “Numerical approach to the risk capital allocation problem, (con Silvia Mayoral), Journal of Risk (2021).
  • “How dark is the dark side of diversification?, (con Pedro Cadenas y Hyun W. Park), Journal of Risk Finance (2021).

 

 

Libros

  • “Hamiltonian Flows and Evolution Semigroups”. Longman Academic Scientific and Technical Research Notes in Mathematics, 1995.
  • “The Method of Maximum Entropy”, World Scientific Publishers, Series: Advances in Mathem. For Applied Sciences 1995.
  • “Linear Inverse Problems: The Maxentropic Connection”World Scientic Publishers, Singapore, 2011. (Disponible en http://www.etjaynescenter.org/software.html)
  • “Diffusions and Waves. Publicado en la serie Mathematics and its Applications de Kluwer Acad. Pubs. Noviembre 2002. (Disponible en Research Gate)
  • Co-editor de “Recent Advances in Applied Probability”, Publicado por Springer-Verlag, Berlin, 2005.
  • “Loss Data Analysis: The Maximum Entropy Approach”, (con Erika Gomes-Gon¸calves y Silvia Mayoral), DeGruyter, Berlin, 2018.

 

Notas de curso

  • “Derivados financieros: curso básico” Notas de curso dictado en las maestrías en la USB, en doctorado de la UC3M y en la XIX-Escuela Venezolana de Matemáticas. Publicado en la serie Libros Profesionales, Editorial Minerva, El Nacional, Caracas 2007.
  • “Fundamentos matemáticos de la teoría de riesgo financiero” Notas de curso sobre medición de riesgo. Cursos dictados en Caracas y Medellín.
  • “Tasas de interés y derivados asociados” (Con Alexander Silva) Notas de curso dictado en Caracas.

 

Libros Reseñados

  • “Point Process Models of Cavity Radiation and Detection”, (S. K. Srinivasan) “Disequilibrium and Self- Organisation”. C.W. Kilmister (ed.)
  • “Noise Induced Transitions” by W. Horsthermke and R. Lefever.
  • “The Fokker-Plank Equation” by H. Risken.
  • “Information and Self- Organisation”. by H. Haken.
  • “Introduction to Probabilistic Modelling” by Pierre Bremaud.
  • “The Mathematics of Random Phenomena” by P. Kree and C. Soize.
  • “Stochastic equations for Complex Systems”. by A. Skorohod.
  • “Modelling Dynamical Phenomena in Cellular Biology”, by L.A.Segel.
  • “Mathematical Biology” by J. D. Murray.
  • “A Maximum Entropy Collection” (5 Vols.).
  • “An Applied Mathematics Collection” (6 Vols.).
  • “A Mathematics Collection” (13 Vols.).
  • “Chaos in Quantum and Classical Mechanics” (M. Gutzwiler)
  • “Chaotic Dynamics in Economic Models” (C. Hommes)
  • “Chaos and Socio Spacial Dynamics” (D. Dedrinos and M. Sonis)
  • “The Transition to Chaos”, (L. Reichl)
  • “The generalized Feller Equation and related Topics) (S. K. Lehnigk)
  • “Probability Theory” (V. Borkar)
  • “Regularizatiuon of Inverse problems” (Engel, Hanke & Neubauer)
  • “Random Evolutions and their Applications” (A. Swishchuk)
  • “Short memory linear processes and econometric applications” (K.T. Mynbaev)

  • 2019: Premio Lorenzo Mendoza Fleury (Área: Matemáticas)
  • 1993: Premio Nacional de Ciencias, (Área: Matemáticas)