An algebraic operator approach to the analysis of Gerber-Shiu functions

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value problems, amounting to iteratively solving first-order problems. This leads to an explicit expression for the Gerber-Shiu function in terms of the penalty function.

Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case

We address the performance optimization problem in a single-stationmulticlass queueing network with changeover times by means of theachievable region approach. This approach seeks to obtainperformance bounds and scheduling policies from the solution of amathematical program over a relaxation of the system's performanceregion. Relaxed formulations (including linear, convex, nonconvexand positive semidefinite constraints) of this region are developedby formulating equilibrium relations satisfied by the system, withthe help of Palm calculus. Our contributions include: (1) newconstraints formulating equilibrium relations on server dynamics;(2) a flow conservation interpretation of the constraintspreviously derived by the potential function method; (3) newpositive semidefinite constraints; (4) new work decomposition lawsfor single-station multiclass queueing networks, which yield newconvex constraints; (5) a unified buffer occupancy method ofperformance analysis obtained from the constraints; (6) heuristicscheduling policies from the solution of the relaxations.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical {\sc vc} dimension, empirical {\sc vc} entropy, andmargin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

Automatització d'una planta de processos químics

Resum L’any 1969 es van començar a comercialitzar els sistemes digitals programables coneguts com autòmats programables o PLC’s, utilitzats per controlar qualsevol tipus de procés industrial. Al llarg de tots aquests anys, aquests sistemes i tota la tecnologia en general han evolucionat molt, i només és qüestió de temps que la tecnologia que utilitzem avui en dia quedi obsoleta i substituïda per una de millors característiques i amb més avantatges. Aquest és el motiu de l’elaboració d’aquest treball, que com a objectiu pretén modernitzar un procés de fabricació d’una industria química que ha quedat molt limitat a causa de l’antiguitat de la instal•lació. Per dur a terme aquesta modernització, s’introdueixen sistemes de control amb majors prestacions, s’utilitzen xarxes de comunicacions per facilitar el muntatge elèctric de la instal•lació i un sistema de supervisió i adquisició de dades per poder obtenir un control més estricte del procés de fabricació i de tots els factors que intervenen. El funcionament del procés de fabricació és que a partir d’unes matèries primeres líquides emmagatzemades en dipòsits, es dosifiquin aquestes matèries en l’ordre i la quantitat desitjada dins un o diversos recipients per barrejar-les i aplicar els tractaments que siguin necessaris. Tot aquest procés està controlat per un autòmat programable, i disposa de diferents terminals operadors per poder interactuar amb el sistema. També té implementat un sistema SCADA en diversos ordinadors per aportar una visió general de la planta en temps real, un registre de dades dels paràmetres que es controlen i alhora serveix per enllaçar amb la xarxa d’ordinadors existent. Com annex d’aquest treball, es presenten els esquemes elèctrics i el programa de l’autòmat programable per veure totes les característiques elèctriques dels dispositius i el mètode de funcionament del procés. S’ha aconseguit donar un salt tecnològic i poder gaudir de tots els avantatges que ofereixen les noves tecnologies, que com a resultat s’ha optimitzat i millorat el procés de fabricació. De totes les conclusions, la més destacada és la d’haver dissenyat un sistema de control basat en una estructura descentralitzada molt flexible, que es pot expandir i adaptar fàcilment als possibles canvis.

Structural macro factors and the affine term structure of interest rates

This work consists of three essays investigating the ability of structural macroeconomic models to price zero coupon U.S. government bonds. 1. A small scale 3 factor DSGE model implying constant term premium is able to provide reasonable a fit for the term structure only at the expense of the persistence parameters of the structural shocks. The test of the structural model against one that has constant but unrestricted prices of risk parameters shows that the exogenous prices of risk-model is only weakly preferred. We provide an MLE based variance-covariance matrix of the Metropolis Proposal Density that improves convergence speeds in MCMC chains. 2. Affine in observable macro-variables, prices of risk specification is excessively flexible and provides term-structure fit without significantly altering the structural parameters. The exogenous component of the SDF is separating the macro part of the model from the term structure and the good term structure fit has as a driving force an extremely volatile SDF and an implied average short rate that is inexplicable. We conclude that the no arbitrage restrictions do not suffice to temper the SDF, thus there is need for more restrictions. We introduce a penalty-function methodology that proves useful in showing that affine prices of risk specifications are able to reconcile stable macro-dynamics with good term structure fit and a plausible SDF. 3. The level factor is reproduced most importantly by the preference shock to which it is strongly and positively related but technology and monetary shocks, with negative loadings, are also contributing to its replication. The slope factor is only related to the monetary policy shocks and it is poorly explained. We find that there are gains in in- and out-of-sample forecast of consumption and inflation if term structure information is used in a time varying hybrid prices of risk setting. In-sample yield forecast are better in models with non-stationary shocks for the period 1982-1988. After this period, time varying market price of risk models provide better in-sample forecasts. For the period 2005-2008, out of sample forecast of consumption and inflation are better if term structure information is incorporated in the DSGE model but yields are better forecasted by a pure macro DSGE model.

Ruin and related quantities in some advanced insurance risk models

Risk theory has been a very active research area over the last decades. The main objectives of the theory are to find adequate stochastic processes which can model the surplus of a (non-life) insurance company and to analyze the risk related quantities such as ruin time, ruin probability, expected discounted penalty function and expected discounted dividend/tax payments. The study of these ruin related quantities provides crucial information for actuaries and decision makers. This thesis consists of the study of four different insurance risk models which are essentially related. The ruin and related quantities are investigated by using different techniques, resulting in explicit or asymptotic expressions for the ruin time, the ruin probability, the expected discounted penalty function and the expected discounted tax payments. - La recherche en théorie du risque a été très dynamique au cours des dernières décennies. D'un point de vue théorique, les principaux objectifs sont de trouver des processus stochastiques adéquats permettant de modéliser le surplus d'une compagnie d'assurance non vie et d'analyser les mesures de risque, notamment le temps de ruine, la probabilité de ruine, l'espérance de la valeur actuelle de la fonction de pénalité et l'espérance de la valeur actuelle des dividendes et taxes. L'étude de ces mesures associées à la ruine fournit des informations cruciales pour les actuaires et les décideurs. Cette thèse consiste en l'étude des quatre différents modèles de risque d'assurance qui sont essentiellement liés. La ruine et les mesures qui y sont associées sont examinées à l'aide de différentes techniques, ce qui permet d'induire des expressions explicites ou asymptotiques du temps de ruine, de la probabilité de ruine, de l'espérance de la valeur actuelle de la fonction de pénalité et l'espérance de la valeur actuelle des dividendes et taxes.

Modeling morphogen gradient formation from arbitrary realistically shaped sources.

Much of the analytical modeling of morphogen profiles is based on simplistic scenarios, where the source is abstracted to be point-like and fixed in time, and where only the steady state solution of the morphogen gradient in one dimension is considered. Here we develop a general formalism allowing to model diffusive gradient formation from an arbitrary source. This mathematical framework, based on the Green's function method, applies to various diffusion problems. In this paper, we illustrate our theory with the explicit example of the Bicoid gradient establishment in Drosophila embryos. The gradient formation arises by protein translation from a mRNA distribution followed by morphogen diffusion with linear degradation. We investigate quantitatively the influence of spatial extension and time evolution of the source on the morphogen profile. For different biologically meaningful cases, we obtain explicit analytical expressions for both the steady state and time-dependent 1D problems. We show that extended sources, whether of finite size or normally distributed, give rise to more realistic gradients compared to a single point-source at the origin. Furthermore, the steady state solutions are fully compatible with a decreasing exponential behavior of the profile. We also consider the case of a dynamic source (e.g. bicoid mRNA diffusion) for which a protein profile similar to the ones obtained from static sources can be achieved.

Some optimization and decision problems in proportional reinsurance

Reinsurance is one of the tools that an insurer can use to mitigate the underwriting risk and then to control its solvency. In this paper, we focus on the proportional reinsurance arrangements and we examine several optimization and decision problems of the insurer with respect to the reinsurance strategy. To this end, we use as decision tools not only the probability of ruin but also the random variable deficit at ruin if ruin occurs. The discounted penalty function (Gerber & Shiu, 1998) is employed to calculate as particular cases the probability of ruin and the moments and the distribution function of the deficit at ruin if ruin occurs.

Modeling reaction kinetics and mass transfer in ozonation in water solutions

This dissertation is based on four articles dealing with modeling of ozonation. The literature part of this considers some models for hydrodynamics in bubble column simulation. A literature review of methods for obtaining mass transfer coefficients is presented. The methods presented to obtain mass transfer are general models and can be applied to any gas-liquid system. Ozonation reaction models and methods for obtaining stoichiometric coefficients and reaction rate coefficients for ozonation reactions are discussed in the final section of the literature part. In the first article, ozone gas-liquid mass transfer into water in a bubble column was investigated for different pH values. A more general method for estimation of mass transfer and Henry’s coefficient was developed from the Beltrán method. The ozone volumetric mass transfer coefficient and the Henry’s coefficient were determined simultaneously by parameter estimation using a nonlinear optimization method. A minor dependence of the Henry’s law constant on pH was detected at the pH range 4 - 9. In the second article, a new method using the axial dispersion model for estimation of ozone self-decomposition kinetics in a semi-batch bubble column reactor was developed. The reaction rate coefficients for literature equations of ozone decomposition and the gas phase dispersion coefficient were estimated and compared with the literature data. The reaction order in the pH range 7-10 with respect to ozone 1.12 and 0.51 the hydroxyl ion were obtained, which is in good agreement with literature. The model parameters were determined by parameter estimation using a nonlinear optimization method. Sensitivity analysis was conducted using object function method to obtain information about the reliability and identifiability of the estimated parameters. In the third article, the reaction rate coefficients and the stoichiometric coefficients in the reaction of ozone with the model component p-nitrophenol were estimated at low pH of water using nonlinear optimization. A novel method for estimation of multireaction model parameters in ozonation was developed. In this method the concentration of unknown intermediate compounds is presented as a residual COD (chemical oxygen demand) calculated from the measured COD and the theoretical COD for the known species. The decomposition rate of p-nitrophenol on the pathway producing hydroquinone was found to be about two times faster than the p-nitrophenol decomposition rate on the pathway producing 4- nitrocatechol. In the fourth article, the reaction kinetics of p-nitrophenol ozonation was studied in a bubble column at pH 2. Using the new reaction kinetic model presented in the previous article, the reaction kinetic parameters, rate coefficients, and stoichiometric coefficients as well as the mass transfer coefficient were estimated with nonlinear estimation. The decomposition rate of pnitrophenol was found to be equal both on the pathway producing hydroquinone and on the path way producing 4-nitrocathecol. Comparison of the rate coefficients with the case at initial pH 5 indicates that the p-nitrophenol degradation producing 4- nitrocathecol is more selective towards molecular ozone than the reaction producing hydroquinone. The identifiability and reliability of the estimated parameters were analyzed with the Marcov chain Monte Carlo (MCMC) method. @All rights reserved. No part of the publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the author.

Automatització d'una planta de processos químics

Resum L’any 1969 es van començar a comercialitzar els sistemes digitals programables coneguts com autòmats programables o PLC’s, utilitzats per controlar qualsevol tipus de procés industrial. Al llarg de tots aquests anys, aquests sistemes i tota la tecnologia en general han evolucionat molt, i només és qüestió de temps que la tecnologia que utilitzem avui en dia quedi obsoleta i substituïda per una de millors característiques i amb més avantatges. Aquest és el motiu de l’elaboració d’aquest treball, que com a objectiu pretén modernitzar un procés de fabricació d’una industria química que ha quedat molt limitat a causa de l’antiguitat de la instal•lació. Per dur a terme aquesta modernització, s’introdueixen sistemes de control amb majors prestacions, s’utilitzen xarxes de comunicacions per facilitar el muntatge elèctric de la instal•lació i un sistema de supervisió i adquisició de dades per poder obtenir un control més estricte del procés de fabricació i de tots els factors que intervenen. El funcionament del procés de fabricació és que a partir d’unes matèries primeres líquides emmagatzemades en dipòsits, es dosifiquin aquestes matèries en l’ordre i la quantitat desitjada dins un o diversos recipients per barrejar-les i aplicar els tractaments que siguin necessaris. Tot aquest procés està controlat per un autòmat programable, i disposa de diferents terminals operadors per poder interactuar amb el sistema. També té implementat un sistema SCADA en diversos ordinadors per aportar una visió general de la planta en temps real, un registre de dades dels paràmetres que es controlen i alhora serveix per enllaçar amb la xarxa d’ordinadors existent. Com annex d’aquest treball, es presenten els esquemes elèctrics i el programa de l’autòmat programable per veure totes les característiques elèctriques dels dispositius i el mètode de funcionament del procés. S’ha aconseguit donar un salt tecnològic i poder gaudir de tots els avantatges que ofereixen les noves tecnologies, que com a resultat s’ha optimitzat i millorat el procés de fabricació. De totes les conclusions, la més destacada és la d’haver dissenyat un sistema de control basat en una estructura descentralitzada molt flexible, que es pot expandir i adaptar fàcilment als possibles canvis.

Adaptive control of Hydraulic Drive

Adaptive control systems are one of the most significant research directions of modern control theory. It is well known that every mechanical appliance’s behavior noticeably depends on environmental changes, functioning-mode parameter changes and changes in technical characteristics of internal functional devices. An adaptive controller involved in control process allows reducing an influence of such changes. In spite of this such type of control methods is applied seldom due to specifics of a controller designing. The work presented in this paper shows the design process of the adaptive controller built by Lyapunov’s function method for the Hydraulic Drive. The calculation needed and the modeling were conducting with MATLAB® software including Simulink® and Symbolic Math Toolbox™ etc. In the work there was applied the Jacobi matrix linearization of the object’s mathematical model and derivation of the suitable reference models based on Newton’s characteristic polynomial. The intelligent adaptive to nonlinearities algorithm for solving Lyapunov’s equation was developed. Developed algorithm works properly but considered plant is not met requirement of functioning with. The results showed confirmation that adaptive systems application significantly increases possibilities in use devices and might be used for correction a system’s behavior dynamics.

A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

On the anharmonic, multi-phonon, Debye-Waller contributions to the phonon-limited resistivity of metals : applications to Na and K

The anharmonic, multi-phonon (MP), and Oebye-Waller factor (OW) contributions to the phonon limited resistivity (;0) of metals derived by Shukla and Muller (1979) by the doubletime temperature dependent Green function method have been numerically evaluated for Na and K in the high temperature limit. The anharmonic contributions arise from the cubic and quartic shift of phonons (CS, QS), and phonon width (W) and the interference term (1). The QS, MP and OW contributions to I' are also derived by the matrix element method and the results are in agreement with those of Shukla and Muller (1979). In the high temperature limit, the contributions to;O from each of the above mentioned terms are of the type BT2 For numerical calculations suitable expressions are derived for the anharmonic contributions to ~ in terms of the third and fourth rank tensors obtained by the Ewald procedure. The numerical calculation of the contributions to;O from the OW, MP term and the QS have been done exactly and from the CS, Wand I terms only approximately in the partial and total Einstein approximations (PEA, TEA), using a first principle approach (Shukla and Taylor (1976)). The results obtained indicate that there is a strong pairwise cancellation between the: OW and MP terms, the QS and CS and the Wand I terms. The sum total of these contributions to;O for Na and K amounts to 4 to 11% and 2 to 7%, respectively, in the PEA while in the TEA they amount to 3 to 7% and 1 to 4%, respectively, in the temperature range.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Phonon dispersion curves and atomic mean square displacement for several fcc and bcc materials

The atomic mean square displacement (MSD) and the phonon dispersion curves (PDC's) of a number of face-centred cubic (fcc) and body-centred cubic (bcc) materials have been calclllated from the quasiharmonic (QH) theory, the lowest order (A2 ) perturbation theory (PT) and a recently proposed Green's function (GF) method by Shukla and Hiibschle. The latter method includes certain anharmonic effects to all orders of anharmonicity. In order to determine the effect of the range of the interatomic interaction upon the anharmonic contributions to the MSD we have carried out our calculations for a Lennard-Jones (L-J) solid in the nearest-neighbour (NN) and next-nearest neighbour (NNN) approximations. These results can be presented in dimensionless units but if the NN and NNN results are to be compared with each other they must be converted to that of a real solid. When this is done for Xe, the QH MSD for the NN and NNN approximations are found to differ from each other by about 2%. For the A2 and GF results this difference amounts to 8% and 7% respectively. For the NN case we have also compared our PT results, which have been calculated exactly, with PT results calculated using a frequency-shift approximation. We conclude that this frequency-shift approximation is a poor approximation. We have calculated the MSD of five alkali metals, five bcc transition metals and seven fcc transition metals. The model potentials we have used include the Morse, modified Morse, and Rydberg potentials. In general the results obtained from the Green's function method are in the best agreement with experiment. However, this improvement is mostly qualitative and the values of MSD calculated from the Green's function method are not in much better agreement with the experimental data than those calculated from the QH theory. We have calculated the phonon dispersion curves (PDC's) of Na and Cu, using the 4 parameter modified Morse potential. In the case of Na, our results for the PDC's are in poor agreement with experiment. In the case of eu, the agreement between the tlleory and experiment is much better and in addition the results for the PDC's calclliated from the GF method are in better agreement with experiment that those obtained from the QH theory.