Some Applications of Markov Additive Processes as Models in Insurance and Financial Mathematics

Cette thèse est principalement constituée de trois articles traitant des processus markoviens additifs, des processus de Lévy et d'applications en finance et en assurance. Le premier chapitre est une introduction aux processus markoviens additifs (PMA), et une présentation du problème de ruine et de notions fondamentales des mathématiques financières. Le deuxième chapitre est essentiellement l'article "Lévy Systems and the Time Value of Ruin for Markov Additive Processes" écrit en collaboration avec Manuel Morales et publié dans la revue European Actuarial Journal. Cet article étudie le problème de ruine pour un processus de risque markovien additif. Une identification de systèmes de Lévy est obtenue et utilisée pour donner une expression de l'espérance de la fonction de pénalité actualisée lorsque le PMA est un processus de Lévy avec changement de régimes. Celle-ci est une généralisation des résultats existant dans la littérature pour les processus de risque de Lévy et les processus de risque markoviens additifs avec sauts "phase-type". Le troisième chapitre contient l'article "On a Generalization of the Expected Discounted Penalty Function to Include Deficits at and Beyond Ruin" qui est soumis pour publication. Cet article présente une extension de l'espérance de la fonction de pénalité actualisée pour un processus subordinateur de risque perturbé par un mouvement brownien. Cette extension contient une série de fonctions escomptée éspérée des minima successives dus aux sauts du processus de risque après la ruine. Celle-ci a des applications importantes en gestion de risque et est utilisée pour déterminer la valeur espérée du capital d'injection actualisé. Finallement, le quatrième chapitre contient l'article "The Minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model" écrit en collaboration avec Romuald Hervé Momeya et publié dans la revue Asia-Pacific Financial Market. Cet article présente de nouveaux résultats en lien avec le problème de l'incomplétude dans un marché financier où le processus de prix de l'actif risqué est décrit par un modèle exponentiel markovien additif. Ces résultats consistent à charactériser la mesure martingale satisfaisant le critère de l'entropie. Cette mesure est utilisée pour calculer le prix d'une option, ainsi que des portefeuilles de couverture dans un modèle exponentiel de Lévy avec changement de régimes.

A risk model with an observer in a Markov environment

We consider a spectrally-negative Markov additive process as a model of a risk process in a random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees the process as negative, where the observation rate may depend on the state of the environment. Using an approximation argument and spectral theory, we establish an explicit formula for the resulting survival probabilities in this general setting. We also discuss an efficient evaluation of the involved quantities and provide a numerical illustration.

Cure Induced Residual Stresses on Thick Composite Components Manufactured by Additive Process

This study investigates the effect of an additive process in manufacturing of thick composites. Airstone 780 E epoxy resin and 785H Hardener system is used in the analysis since it is widely used wind turbine blade, namely thick components. As a fiber, fabric by SAERTEX (812 g/m2) with a 0-90 degrees layup direction is used. Temperature overshoot is a major issue during the manufacturing of thick composites. A high temperature overshoot leads to an increase in residual stresses. These residual stresses are causing warping, delamination, dimensional instability, and undesired distortion of composite structures. A coupled thermo-mechanical model capable of predicting cure induced residual stresses have been built using the commercial FE software Abaqus®. The possibility of building thick composite components by means of adding a finite number of sub-laminates has been investigated. The results have been compared against components manufactured following a standard route. The influence of pre-curing of the sub-laminates has also been addressed and results compared with standard practice. As a result of the study, it is found that introducing additive process can prevent temperature overshoot to occur and benefits the residual stresses generation during the curing process. However, the process time required increases by 50%, therefore increasing the manufacturing costs. An optimized cure cycle is required to minimize process time and cure induced defects simultaneously.

Efficient simulation of a Tandem Jackson Network

The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level L before it becomes empty, starting from a given state. The approach is based on a Markov additive process representation of the buffer processes, leading to an exponential change of measure to be used in an importance sampling procedure. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer. We prove that when the first buffer is finite, this method yields asymptotically efficient simulation for any set of arrival and service rates. In fact, the relative error is bounded independent of the level L; a new result which is not established for any other known method. When the first buffer is infinite, we propose a natural extension of the exponential change of measure for the finite buffer case. In this case, the relative error is shown to be bounded (independent of L) only when the second server is the bottleneck; a result which is known to hold for some other methods derived through large deviations analysis. When the first server is the bottleneck, experimental results using our method seem to suggest that the relative error is bounded linearly in L.

Les processus additifs markoviens et leurs applications en finance mathématique

Cette thèse porte sur les questions d'évaluation et de couverture des options dans un modèle exponentiel-Lévy avec changements de régime. Un tel modèle est construit sur un processus additif markovien un peu comme le modèle de Black- Scholes est basé sur un mouvement Brownien. Du fait de l'existence de plusieurs sources d'aléa, nous sommes en présence d'un marché incomplet et ce fait rend inopérant les développements théoriques initiés par Black et Scholes et Merton dans le cadre d'un marché complet. Nous montrons dans cette thèse que l'utilisation de certains résultats de la théorie des processus additifs markoviens permet d'apporter des solutions aux problèmes d'évaluation et de couverture des options. Notamment, nous arrivons à caracté- riser la mesure martingale qui minimise l'entropie relative à la mesure de probabilit é historique ; aussi nous dérivons explicitement sous certaines conditions, le portefeuille optimal qui permet à un agent de minimiser localement le risque quadratique associé. Par ailleurs, dans une perspective plus pratique nous caract érisons le prix d'une option Européenne comme l'unique solution de viscosité d'un système d'équations intégro-di érentielles non-linéaires. Il s'agit là d'un premier pas pour la construction des schémas numériques pour approcher ledit prix.

Additive Manufacturing by LPBF and WAAM of metals: correlation between production process, microstructure and mechanical properties

In the most recent years, Additive Manufacturing (AM) has drawn the attention of both academic research and industry, as it might deeply change and improve several industrial sectors. From the material point of view, AM results in a peculiar microstructure that strictly depends on the conditions of the additive process and directly affects mechanical properties. The present PhD research project aimed at investigating the process-microstructure-properties relationship of additively manufactured metal components. Two technologies belonging to the AM family were considered: Laser-based Powder Bed Fusion (LPBF) and Wire-and-Arc Additive Manufacturing (WAAM). The experimental activity was carried out on different metals of industrial interest: a CoCrMo biomedical alloy and an AlSi7Mg0.6 alloy processed by LPBF, an AlMg4.5Mn alloy and an AISI 304L austenitic stainless steel processed by WAAM. In case of LPBF, great attention was paid to the influence that feedstock material and process parameters exert on hardness, morphological and microstructural features of the produced samples. The analyses, targeted at minimizing microstructural defects, lead to process optimization. For heat-treatable LPBF alloys, innovative post-process heat treatments, tailored on the peculiar hierarchical microstructure induced by LPBF, were developed and deeply investigated. Main mechanical properties of as-built and heat-treated alloys were assessed and they were well-correlated to the specific LPBF microstructure. Results showed that, if properly optimized, samples exhibit a good trade-off between strength and ductility yet in the as-built condition. However, tailored heat treatments succeeded in improving the overall performance of the LPBF alloys. Characterization of WAAM alloys, instead, evidenced the microstructural and mechanical anisotropy typical of AM metals. Experiments revealed also an outstanding anisotropy in the elastic modulus of the austenitic stainless-steel that, along with other mechanical properties, was explained on the basis of microstructural analyses.

Using Normative Markov Decision Processes for Evaluating Electronic Contracts: A Case Study in a Simulated Aerospace Aftermarket

Before signing electronic contracts, a rational agent should estimate the expected utilities of these contracts and calculate the violation risks related to them. In order to perform such pre-signing procedures, this agent has to be capable of computing a policy taking into account the norms and sanctions in the contracts. In relation to this, the contribution of this work is threefold. First, we present the Normative Markov Decision Process, an extension of the Markov Decision Process for explicitly representing norms. In order to illustrate the usage of our framework, we model an example in a simulated aerospace aftermarket. Second, we specify an algorithm for identifying the states of the process which characterize the violation of norms. Finally, we show how to compute policies with our framework and how to calculate the risk of violating the norms in the contracts by adopting a particular policy.

Green-Markov models - new optimization strategies: a case study for user allocation in co-channel macro/femto networks

ABSTRACT: The femtocell concept aims to combine fixed-line broadband access with mobile telephony using the deployment of low-cost, low-power third and fourth generation base stations in the subscribers' homes. While the self-configuration of femtocells is a plus, it can limit the quality of service (QoS) for the users and reduce the efficiency of the network, based on outdated allocation parameters such as signal power level. To this end, this paper presents a proposal for optimized allocation of users on a co-channel macro-femto network, that enable self-configuration and public access, aiming to maximize the quality of service of applications and using more efficiently the available energy, seeking the concept of Green networking. Thus, when the user needs to connect to make a voice or a data call, the mobile phone has to decide which network to connect, using the information of number of connections, the QoS parameters (packet loss and throughput) and the signal power level of each network. For this purpose, the system is modeled as a Markov Decision Process, which is formulated to obtain an optimal policy that can be applied on the mobile phone. The policy created is flexible, allowing different analyzes, and adaptive to the specific characteristics defined by the telephone company. The results show that compared to traditional QoS approaches, the policy proposed here can improve energy efficiency by up to 10%.

Green markov - uma abordagem híbrida de política markoviana e simulação discreta para planejamento de alocação de usuários em redes macro-femto

O uso da comunicação de voz e dados através de dispositivos móveis vem aumentando significativamente nos últimos anos. Tal expansão traz algumas dificuldades inerentes, tais como: ampliação constante de capacidade das redes e eficiência energética. Neste contexto, vem se consolidando o conceito de Green networks, que se concentra no esforço para economia de energia e redução de CO2. Neste sentido, este trabalho propõe validar um modelo de uma política baseado em processo markoviano de decisão, visando a otimizar o consumo de energia, QoS e QoE, na alocação de usuários em redes macrocell e femtocell. Para isso o modelo foi inserido no simulador NS-2, aliando a solução analítica markoviana à flexibilidade característica da simulação discreta. A partir dos resultados apresentados na simulação, a política obteve uma economia significativa no consumo energético, melhorando a eficiência energética em até 4%, além de melhorar a qualidade de serviço em relação às redes macrocell e femtocell, demonstrando-se eficaz, de modo a alterar diretamente as métricas de QoS e de QoE.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

A New Class of Processes for Formalizing and Generalizing Individual-Based Models: The Semi-Semi-Markov Processes

2000 Mathematics Subject Classification: 60K15, 60K20, 60G20,60J75, 60J80, 60J85, 60-08, 90B15.

A hybrid approach to multi-agent decision-making

In the aftermath of a large-scale disaster, agents' decisions derive from self-interested (e.g. survival), common-good (e.g. victims' rescue) and teamwork (e.g. fire extinction) motivations. However, current decision-theoretic models are either purely individual or purely collective and find it difficult to deal with motivational attitudes; on the other hand, mental-state based models find it difficult to deal with uncertainty. We propose a hybrid, CvI-JI, approach that combines: i) collective 'versus' individual (CvI) decisions, founded on the Markov decision process (MDP) quantitative evaluation of joint-actions, and ii)joint-intentions (JI) formulation of teamwork, founded on the belief-desire-intention (BDI) architecture of general mental-state based reasoning. The CvI-JI evaluation explores the performance's improvement

Disseny i caracterització d'estructures RF amb printed electronics per a RFID

En els últims anys printed electronics està aixecant un gran interès entre la indústria electrònica. Aquest tipus de procés consisteix en imprimir circuits amb tècniques d'impressió convencionals utilitzant tintes conductores, resistives, dielèctriques o semiconductores sobre substrats flexibles de baix cost com paper o plàstic. Fer servir aquestes tècniques s'espera que suposi una reducció dels costos de producció degut a que és un procés totalment additiu el que fa que sigui més senzill i es redueixi la quantitat de material emprat. El disseny de dispositius bàsics com resistències, condensadors i bobines per posteriorment veure la relació entre simulacions i valors obtinguts ha ocupat la primera part del projecte. La segona s’ha centrat en fer prototips d’antenes per a RFID (Radio Frequency IDentification) amb la tecnologia que es disposa a CEPHIS (Centre de Prototips i Solucions Hardwre-Software). Tot això ha servit per caracteritzar la tecnologia de la que es disposa i saber en quins apartats s’ha de seguir treballant per aconseguir millors prestacions.

Potkurilaitteen ohjausputken laserpinnoitus

Laserpinnoitus on additiivinen prosessi, jossa lasertehon avulla sulatetaan pinnoitusainetta pinnoitettavan kappaleen pintaan. Laserpinnoituksella on mahdollista aikaansaada tiivis sekä kova, kulutusta ja korroosiota kestävä pinnoite kappaleen pintaan. Tässä työssä kohteena oli potkurilaitteen ohjausputken laserpinnoitus. Kyseisessä kohteessa pinnoitteelta vaaditaan hyvää korroosion- ja kulumisen kestoa. Työn tavoitteena oli lisätä tietoisuutta laserpinnoitusprosessista ja siinä vaikuttavista tekijöistä. Myös materiaaliominaisuuksien vaikutuksia sekä pinnoitus- että pinnoitettavien aineiden osalta selvitettiin. Työhön sisältyi myös kokeellinen osuus, jossa tavoitteena oli löytää kustannustehokkain pinnoiteaine tutkittuun kohteeseen. Kokeissa ohjausputki- sekä levyaihioon tehtiin koepinnoituksia. Kokeiden ja edelleen materiaalitutkimuksien avulla tutkittiin neljää eri pinnoitusainetta, jotka olivat Stellitti 21, Inconel 625, AISI 316L ja AISI 431. Kovuus- ja taivutuskokeiden perusteella kyseisistä aineista vain Stelliitti 21 täytti ohjausputken pinnoitteelle asetetut vaatimukset. Näin ollen Stelliitti 21 valikoitui kustannustehokkaimmaksi pinnoitusaineeksi ohjausputkien laserpinnoitukseen.

T-Policy in Reliability and Inventory

In this thesis T-policy is implemented to the inventory system with random lead time and also repair in the reliability of k-out-of-n system. Inventory system may be considered as the system of keeping records of the amounts of commodities in stock. Reliability is defined as the ability of an entity to perform a required function under given conditions for a given time interval. It is measured by the probability that an entity E can perform a required function under given conditions for the time interval. In this thesis considered k-out-of-n system with repair and two modes of service under T-policy. In this case first server is available always and second server is activated on elapse of T time units. The lead time is exponentially distributed with parameter  and T is exponentially distributed with parameter  from the epoch at which it was inactivated after completion of repair of all failed units in the previous cycle, or the moment n-k failed units accumulate. The repaired units are assumed to be as good as new. In this study , three different situations, ie; cold system, warm system and hot system. A k-out-of-n system is called cold, warm or hot according as the functional units do not fail, fail at a lower rate or fail at the same rate when system is shown as that when it is up.