Made available in DSpace on 2014-07-29T16:02:17Z (GMT). No. of bitstreams: 1 SILVANA DA SILVA RODRIGUES.pdf: 983315 bytes, checksum: 17ccfa7762b3ec7758b0c81b7ca259bf (MD5) Previous issue date: 2011-01-28 / The main purpose of this dissertation was to construct lower and upper bounds for the cardinality of the error correcting codes for constant-weight, contained in the vector space Fn 3 , where F3 is a field with three elements, knowing parameters such as length and minimum distance code. We present the main results of linear algebra necessary to develop the theory of codes and then the fundamental concepts of more practical class of codes, the linear error correcting codes. We state the Totobola problem and the Football problem, relating them to the theory of codes and present some bounds for the "covering radius problem"for r = 1 , some values of n. In the last chapter, we conclude the work with some examples that illustrate bounds of coverings for Fn 3 , with r = 2 and 3, and the generalization of the problem, where we present the binary covering radius problem, the case of multiple coverages and the extension of the idea, citing bounds for the cardinality of the codes contained in the vector space over a finite field with any arbitrary number of elements. / O principal objetivo desta dissertação foi construir limitantes inferiores e superiores para o número de elementos de um código corretor de erros de peso constante, contido no espaço vetorial Fn 3 , onde F3 é um corpo contendo três elementos, a partir de parâmetros como comprimento e distância mínima do código. Apresentamos os principais resultados da álgebra linear necessários ao desenvolvimento da teoria de códigos e em seguida, os conceitos fundamentais da classe de códigos mais conhecida na prática: os códigos lineares. Definimos os problemas do totobola e da piscina de futebol e a relação de ambos, com a teoria de códigos e com o problema do raio de cobertura. Construímos limitantes para o problema do raio de cobertura para r = 1, a partir da variação de n, e no último capítulo o trabalho é finalizado com a apresentação de exemplos que ilustram limitantes de cobertura para Fn 3 , com r = 2 e 3 e a generalização do assunto, onde apresentamos o problema binário do raio de cobertura, o caso das múltiplas coberturas e a extensão da idéia, citando limitantes para o número de elementos de códigos contidos em espaços vetoriais sobre um corpo finito contendo uma quantidade qualquer de elementos.

In this work we study two problems motivated by Risk Management: the optimal design of financial products from an investor's point of view and the calculation of bounds and approximations for sums involving non-independent random variables. The element that interconnects these two topics is the notion of conditioning, a fundamental concept in probability and statistics which appears to be a useful device in finance. In the first part of the dissertation, we analyse structured products that are now widespread in the banking and insurance industry. These products typically protect the investor against bearish stock markets while offering upside participation when the markets are bullish. Examples of these products include capital guaranteed funds commercialised by banks, and equity linked contracts sold by insurers. The design of these products is complex in general and it is vital to examine to which extent they are actually interesting from the investor's point of view and whether they cannot be dominated by other strategies. In the academic literature on structured products the focus has been almost exclusively on the pricing and hedging of these instruments and less on their performance from an investor's point of view. In this work we analyse the attractiveness of these products. We assess the theoretical cost of inefficiency when buying a structured product and describe the optimal strategy explicitly if possible. Moreover we examine the cost of the inefficiency in practice. We extend the results of Dybvig (1988a, 1988b) and Cox & Leland (1982, 2000) who in the context of a complete, one-dimensional market investigated the inefficiency of path-dependent pay-offs. In the dissertation we consider this problem in one-dimensional Levy and multidimensional Black-Scholes financial markets and we provide evidence that path-dependent pay-offs should not be preferred by decision makers with a fixed investment horizon, and they should buy path-independent structures instead. In these market settings we also demonstrate the optimal contract that provides the given distribution to the consumer, and in the case of risk- averse investors we are able to propose two ways of improving the design of financial products. Finally we illustrate the theory with a few well-known securities and strategies e.g. dollar cost averaging, buy-and-hold investments and widely used portfolio insurance strategies. The second part of the dissertation considers the problem of finding the distribution of a sum of non- independent random variables. Such dependent sums appear quite often in insurance and finance, for instance in case of the aggregate claim distribution or loss distribution of an investment portfolio. An interesting avenue to cope with this problem consists in using so-called convex bounds, studied by Dhaene et al. (2002a, 2002b), who applied these to sums of log-normal random variables. In their papers they have shown how these convex bounds can be used to derive closed-form approximations for several of the risk measures of such a sum. In the dissertation we prove that unlike the log-normal case the construction of a convex lower bound in explicit form appears to be out of reach for general sums of log-elliptical risks and we show how we can construct stop-loss bounds and we use these to construct mean preserving approximations for general sums of log-elliptical distributions in explicit form. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Cette thèse traite de processus de détérioration en théorie du risque et en biomathématique.<p><p>En théorie du risque, le processus de détérioration étudié est celui des sinistres supportés par une compagnie d'assurance.<p><p>Le premier chapitre examine la distribution de Markov-Polya comme loi possible pour modéliser le nombre de sinistres et établit certains liens avec la famille de lois de Katz/Panjer. Nous construisons la loi de Markov-Polya sur base d'un modèle de survenance des sinistres et nous montrons qu'elle satisfait une récurrence élégante. Celle-ci permet notamment de déduire un algorithme efficace pour la loi composée correspondante. Nous déduisons la famille de Katz/Panjer comme famille limite de la loi de Markov-Polya.<p><p>Le second chapitre traite de la famille dite "Lagrangian Katz" qui étend celle de Katz/Panjer. Nous motivons par un problème de premier passage son utilisation comme loi du nombre de sinistres. Nous caractérisons toutes les lois qui en font partie et nous déduisons un algorithme efficace pour la loi composée. Nous examinons également son indice de dispersion ainsi que son comportement asymptotique. <p><p>Dans le troisième chapitre, nous étudions la probabilité de ruine sur horizon fini dans un modèle discret avec taux d'intérêt positifs. Nous déterminons un algorithme ainsi que différentes bornes pour cette probabilité. Une borne particulière nous permet de construire deux mesures de risque. Nous examinons également la possibilité de faire appel à de la réassurance proportionelle avec des niveaux de rétention égaux ou différents sur les périodes successives.<p><p>Dans le cadre de processus épidémiques, la détérioration étudiée consiste en la propagation d'une maladie de type SIE (susceptible - infecté - éliminé). La manière dont un infecté contamine les susceptibles est décrite par des distributions de survie particulières. Nous en déduisons la distribution du nombre total de personnes infectées à la fin de l'épidémie. Nous examinons en détails les épidémies dites de type Markov-Polya et hypergéométrique. Nous approximons ensuite cette loi par un processus de branchement. Nous étudions également un processus de détérioration similaire en théorie de la fiabilité où le processus de détérioration consiste en la propagation de pannes en cascade dans un système de composantes interconnectées. <p><p><p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

We prove that there exist three distinct, comprehensive classes of (formal) contexts with polynomially many concepts. Namely: contexts which are nowhere dense, of bounded breadth or highly convex. Already present in G. Birkhoff's classic monograph is the notion of breadth of a lattice; it equals the number of atoms of a largest boolean suborder. Even though it is natural to define the breadth of a context as being that of its concept lattice, this idea had not been exploited before. We do this and establish many equivalences. Amongst them, it is shown that the breadth of a context equals the size of its largest minimal generator, its largest contranominal-scale subcontext, as well as the Vapnik-Chervonenkis dimension of both its system of extents and of intents. The polynomiality of the aforementioned classes is proven via upper bounds (also known as majorants) for the number of maximal bipartite cliques in bipartite graphs. These are results obtained by various authors in the last decades. The fact that they yield statements about formal contexts is a reward for investigating how two established fields interact, specifically Formal Concept Analysis (FCA) and graph theory. We improve considerably the breadth bound. Such improvement is twofold: besides giving a much tighter expression, we prove that it limits the number of minimal generators. This is strictly more general than upper bounding the quantity of concepts. Indeed, it automatically implies a bound on these, as well as on the number of proper premises. A corollary is that this improved result is a bound for the number of implications in the canonical basis too. With respect to the quantity of concepts, this sharper majorant is shown to be best possible. Such fact is established by constructing contexts whose concept lattices exhibit exactly that many elements. These structures are termed, respectively, extremal contexts and extremal lattices. The usual procedure of taking the standard context allows one to work interchangeably with either one of these two extremal structures. Extremal lattices are equivalently defined as finite lattices which have as many elements as possible, under the condition that they obey two upper limits: one for its number of join-irreducibles, other for its breadth. Subsequently, these structures are characterized in two ways. Our first characterization is done using the lattice perspective. Initially, we construct extremal lattices by the iterated operation of finding smaller, extremal subsemilattices and duplicating their elements. Then, it is shown that every extremal lattice must be obtained through a recursive application of this construction principle. A byproduct of this contribution is that extremal lattices are always meet-distributive. Despite the fact that this approach is revealing, the vicinity of its findings contains unanswered combinatorial questions which are relevant. Most notably, the number of meet-irreducibles of extremal lattices escapes from control when this construction is conducted. Aiming to get a grip on the number of meet-irreducibles, we succeed at proving an alternative characterization of these structures. This second approach is based on implication logic, and exposes an interesting link between number of proper premises, pseudo-extents and concepts. A guiding idea in this scenario is to use implications to construct lattices. It turns out that constructing extremal structures with this method is simpler, in the sense that a recursive application of the construction principle is not needed. Moreover, we obtain with ease a general, explicit formula for the Whitney numbers of extremal lattices. This reveals that they are unimodal, too. Like the first, this second construction method is shown to be characteristic. A particular case of the construction is able to force - with precision - a high number of (in the sense of "exponentially many'') meet-irreducibles. Such occasional explosion of meet-irreducibles motivates a generalization of the notion of extremal lattices. This is done by means of considering a more refined partition of the class of all finite lattices. In this finer-grained setting, each extremal class consists of lattices with bounded breadth, number of join irreducibles and meet-irreducibles as well. The generalized problem of finding the maximum number of concepts reveals itself to be challenging. Instead of attempting to classify these structures completely, we pose questions inspired by Turán's seminal result in extremal combinatorics. Most prominently: do extremal lattices (in this more general sense) have the maximum permitted breadth? We show a general statement in this setting: for every choice of limits (breadth, number of join-irreducibles and meet-irreducibles), we produce some extremal lattice with the maximum permitted breadth. The tools which underpin all the intuitions in this scenario are hypergraphs and exact set covers. In a rather unexpected, but interesting turn of events, we obtain for free a simple and interesting theorem about the general existence of "rich'' subcontexts. Precisely: every context contains an object/attribute pair which, after removed, results in a context with at least half the original number of concepts.

Subject of the submitted thesis is the issue of currency options. The aim is the detailed analysis of currency options forcefully on dealing, characteristics, methods of pricing and their use for hedging strategies. The first part of the thesis presents an introduction into the option theory. The second part is about dealing, pricing and arbitrage relationships of currency options. In this part are two option pricing model extracted -- the binomial options pricing model for pricing currency options and the Garman-Kohlhagen model for pricing European currency options. In the third part is an example for a currency put option hedging strategy.

Cette thèse s'inscrit dans le domaine de l'apprentissage statistique. Le cadre principal est celui de la prévision de suites déterministes arbitraires (ou suites individuelles), qui recouvre des problèmes d'apprentissage séquentiel où l'on ne peut ou ne veut pas faire d'hypothèses de stochasticité sur la suite des données à prévoir. Cela conduit à des méthodes très robustes. Dans ces travaux, on étudie quelques liens étroits entre la théorie de la prévision de suites individuelles et le cadre statistique classique, notamment le modèle de régression avec design aléatoire ou fixe, où les données sont modélisées de façon stochastique. Les apports entre ces deux cadres sont mutuels : certaines méthodes statistiques peuvent être adaptées au cadre séquentiel pour bénéficier de garanties déterministes ; réciproquement, des techniques de suites individuelles permettent de calibrer automatiquement des méthodes statistiques pour obtenir des bornes adaptatives en la variance du bruit. On étudie de tels liens sur plusieurs problèmes voisins : la régression linéaire séquentielle parcimonieuse en grande dimension (avec application au cadre stochastique), la régression linéaire séquentielle sur des boules L1, et l'agrégation de modèles non linéaires dans un cadre de sélection de modèles (régression avec design fixe). Enfin, des techniques stochastiques sont utilisées et développées pour déterminer les vitesses minimax de divers critères de performance séquentielle (regrets interne et swap notamment) en environnement déterministe ou stochastique. / The topics addressed in this thesis lie in statistical machine learning. Our main framework is the prediction of arbitrary deterministic sequences (or individual sequences). It includes online learning tasks for which we cannot make any stochasticity assumption on the data to be predicted, which requires robust methods. In this work, we analyze several connections between the theory of individual sequences and the classical statistical setting, e.g., the regression model with fixed or random design, where stochastic assumptions are made. These two frameworks benefit from one another: some statistical methods can be adapted to the online learning setting to satisfy deterministic performance guarantees. Conversely, some individual-sequence techniques are useful to tune the parameters of a statistical method and to get risk bounds that are adaptive to the unknown variance. We study such connections for several connected problems: high-dimensional online linear regression under a sparsity scenario (with an application to the stochastic setting), online linear regression on L1-balls, and aggregation of nonlinear models in a model selection framework (regression on a fixed design). We also use and develop stochastic techniques to compute the minimax rates of game-theoretic online measures of performance (e.g., internal and swap regrets) in a deterministic or stochastic environment.

Dans cette thèse, nous étudions le spectre conforme d'une surface fermée et le spectre de Steklov conforme d'une surface compacte à bord et leur application à la géométrie conforme et à la topologie. Soit (Σ, c) une surface fermée munie d'une classe conforme c. Alors la k-ième valeur propre conforme est définie comme Λ_k(Σ,c)=sup{λ_k(g) Aire(Σ,g)| g ∈ c), où λ_k(g) est la k-ième valeur propre de l'operateur de Laplace-Beltrami de la métrique g sur Σ. Notons que nous commeçons par λ_0(g) = 0. En prennant le supremum sur toutes les classes conformes C sur Σ on obtient l'invariant topologique suivant de Σ: Λ_k(Σ)=sup{Λ_k(Σ,c)| c ∈ C}. D'après l'article [65], les quantités Λ_k(Σ, c) et Λ_k(Σ) sont bien définies. Si une métrique g sur Σ satisfait λ_k(g) Aire(Σ, g) = Λ_k(Σ), alors on dit que g est maximale pour la fonctionnelle λ_k(g) Aire(Σ, g). Dans l'article [73], il a été montré que les métriques maximales pour λ_1(g) Aire(Σ, g) peuvent au pire avoir des singularités coniques. Dans cette thèse nous montrons que les métriques maximales pour les fonctionnelles λ_1(g) Aire(T^2, g) et λ_1(g) Aire(KL, g), où T^2 et KL dénotent le 2-tore et la bouteille de Klein, ne peuvent pas avoir de singularités coniques. Ce résultat découle d'un théorème de classification de classes conformes par des métriques induites d'une immersion minimale ramifiée dans une sphère ronde aussi montré dans cette thèse. Un autre invariant que nous étudions dans cette thèse est le k-ième invariant de Friedlander-Nadirashvili défini comme: I_k(Σ) = inf{Λ_k(Σ, c)| c ∈ C}. L'invariant I_1(Σ) a été introduit dans l'article [34]. Dans cette thèse nous montrons que pour toute surface orientable et pour toute surface non-orientable de genre impaire I_k(Σ)=I_k(S^2) et pour toute surface non-orientable de genre paire I_k(RP^2) ≥ I_k(Σ)>I_k(S^2). Ici S^2 et RP^2 dénotent la 2-sphère et le plan projectif. Nous conjecturons que I_k(Σ) sont des invariants des cobordismes des surfaces fermées. Le spectre de Steklov conforme est défini de manière similaire. Soit (Σ, c) une surface compacte à bord non vide ∂Σ, alors les k-ièmes valeurs propres de Steklov conformes sont définies comme: σ*_k(Σ, c)=sup{σ_k(g) Longueur(∂Σ, g)| g ∈ c}, où σ_k(g) est la k-ième valeur propre de Steklov de la métrique g sur Σ. Ici nous supposons que σ_0(g) = 0. De façon similaire au problème fermé, on peut définir les quantités suivantes: σ*_k(Σ)=sup{σ*_k(Σ, c)| c ∈ C} et I^σ_k(Σ)=inf{σ*_k(Σ, c)| c ∈ C}. Les résultats de l'article [16] impliquent que toutes ces quantités sont bien définies. Dans cette thèse on obtient une formule pour la limite de σ*_k(Σ, c_n) lorsque la suite des classes conformes c_n dégénère. Cette formule implique que pour toute surface à bord I^σ_k(Σ)= I^σ_k(D^2), où D^2 dénote le 2-disque. On remarque aussi que les quantités I^σ_k(Σ) sont des invariants des cobordismes de surfaces à bord. De plus, on obtient une borne supérieure pour la fonctionnelle σ^k(g) Longueur(∂Σ, g), où Σ est non-orientable, en terme de son genre et le nombre de composants de bord. / In this thesis, we study the conformal spectrum of a closed surface and the conformal Steklov spectrum of a compact surface with boundary and their application to conformal geometry and topology. Let (Σ,c) be a closed surface endowed with a conformal class c then the k-th conformal eigenvalue is defined as Λ_k(Σ,c)=sup{λ_k(g) Aire(Σ,g)| g ∈ c), where λ_k(g) is the k-th Laplace-Beltrami eigenvalue of the metric g on Σ. Note that we start with λ_0(g) = 0 Taking the supremum over all conformal classes C on Σ one gets the following topological invariant of Σ: Λ_k(Σ)=sup{Λ_k(Σ,c)| c ∈ C}. It follows from the paper [65] that the quantities Λ_k(Σ, c) and Λ_k(Σ) are well-defined. Suppose that for a metric g on Σ the following identity holds λ_k(g) Aire(Σ, g) = Λ_k(Σ). Then one says that the metric g is maximal for the functional λ_k(g) Aire(Σ, g). In the paper [73] it was shown that the maximal metrics for the functional λ_1(g) Aire(Σ, g) at worst can have conical singularities. In this thesis we show that the maximal metrics for the functionals λ_1(g) Aire(T^2, g) and λ_1(g) Aire(KL, g), where T^2 and KL stand for the 2-torus and the Klein bottle respectively, cannot have conical singularities. This result is a corollary of a conformal class classification theorem by metrics induced from a branched minimal immersion into a round sphere that we also prove in the thesis. Another invariant that we study in this thesis is the k-th Friedlander-Nadirashvili invariant defined as: I_k(Σ) = inf{Λ_k(Σ, c)| c ∈ C}. The invariant I_1(Σ) was introduced in the paper [34]. In this thesis we prove that for any orientable surface and any non-orientable surface of odd genus I_k(Σ)=I_k(S^2) and for any non-orientable surface of even genus I_k(RP^2) ≥ I_k(Σ)>I_k(S^2). Here S^2 and RP^2 denote the 2-sphere and the projective plane respectively. We also conjecture that I_k(Σ) are invariants of cobordisms of closed manifolds. The conformal Steklov spectrum is defined in a similar way. Let (Σ, c) be a compact surface with non-empty boundary ∂Σ then the k-th conformal Steklov eigenvalues is defined by the formula: σ*_k(Σ, c)=sup{σ_k(g) Longueur(∂Σ, g)| g ∈ c}, where σ_k(g) is the k-th Steklov eigenvalue of the metric g on Σ. Here we suppose that σ_0(g) = 0. Similarly to the closed problem one can define the following quantities: σ*_k(Σ)=sup{σ*_k(Σ, c)| c ∈ C} and I^σ_k(Σ)=inf{σ*_k(Σ, c)| c ∈ C}. The results of the paper [16] imply that all these quantities are well-defined. In this thesis we obtain a formula for the limit of the k-th conformal Steklov eigenvalue when the sequence of conformal classes degenerates. Using this formula we show that for any surface with boundary I^σ_k(Σ)= I^σ_k(D^2), where D^2 stands for the 2-disc. We also notice that I^σ_k(Σ) are invariants of cobordisms of surfaces with boundary. Moreover, we obtain an upper bound for the functional σ^k(g) Longueur(∂Σ, g), where Σ is non-orientable, in terms of its genus and the number of boundary components.

We prove that there exist three distinct, comprehensive classes of (formal) contexts with polynomially many concepts. Namely: contexts which are nowhere dense, of bounded breadth or highly convex. Already present in G. Birkhoff's classic monograph is the notion of breadth of a lattice; it equals the number of atoms of a largest boolean suborder. Even though it is natural to define the breadth of a context as being that of its concept lattice, this idea had not been exploited before. We do this and establish many equivalences. Amongst them, it is shown that the breadth of a context equals the size of its largest minimal generator, its largest contranominal-scale subcontext, as well as the Vapnik-Chervonenkis dimension of both its system of extents and of intents. The polynomiality of the aforementioned classes is proven via upper bounds (also known as majorants) for the number of maximal bipartite cliques in bipartite graphs. These are results obtained by various authors in the last decades. The fact that they yield statements about formal contexts is a reward for investigating how two established fields interact, specifically Formal Concept Analysis (FCA) and graph theory. We improve considerably the breadth bound. Such improvement is twofold: besides giving a much tighter expression, we prove that it limits the number of minimal generators. This is strictly more general than upper bounding the quantity of concepts. Indeed, it automatically implies a bound on these, as well as on the number of proper premises. A corollary is that this improved result is a bound for the number of implications in the canonical basis too. With respect to the quantity of concepts, this sharper majorant is shown to be best possible. Such fact is established by constructing contexts whose concept lattices exhibit exactly that many elements. These structures are termed, respectively, extremal contexts and extremal lattices. The usual procedure of taking the standard context allows one to work interchangeably with either one of these two extremal structures. Extremal lattices are equivalently defined as finite lattices which have as many elements as possible, under the condition that they obey two upper limits: one for its number of join-irreducibles, other for its breadth. Subsequently, these structures are characterized in two ways. Our first characterization is done using the lattice perspective. Initially, we construct extremal lattices by the iterated operation of finding smaller, extremal subsemilattices and duplicating their elements. Then, it is shown that every extremal lattice must be obtained through a recursive application of this construction principle. A byproduct of this contribution is that extremal lattices are always meet-distributive. Despite the fact that this approach is revealing, the vicinity of its findings contains unanswered combinatorial questions which are relevant. Most notably, the number of meet-irreducibles of extremal lattices escapes from control when this construction is conducted. Aiming to get a grip on the number of meet-irreducibles, we succeed at proving an alternative characterization of these structures. This second approach is based on implication logic, and exposes an interesting link between number of proper premises, pseudo-extents and concepts. A guiding idea in this scenario is to use implications to construct lattices. It turns out that constructing extremal structures with this method is simpler, in the sense that a recursive application of the construction principle is not needed. Moreover, we obtain with ease a general, explicit formula for the Whitney numbers of extremal lattices. This reveals that they are unimodal, too. Like the first, this second construction method is shown to be characteristic. A particular case of the construction is able to force - with precision - a high number of (in the sense of "exponentially many'') meet-irreducibles. Such occasional explosion of meet-irreducibles motivates a generalization of the notion of extremal lattices. This is done by means of considering a more refined partition of the class of all finite lattices. In this finer-grained setting, each extremal class consists of lattices with bounded breadth, number of join irreducibles and meet-irreducibles as well. The generalized problem of finding the maximum number of concepts reveals itself to be challenging. Instead of attempting to classify these structures completely, we pose questions inspired by Turán's seminal result in extremal combinatorics. Most prominently: do extremal lattices (in this more general sense) have the maximum permitted breadth? We show a general statement in this setting: for every choice of limits (breadth, number of join-irreducibles and meet-irreducibles), we produce some extremal lattice with the maximum permitted breadth. The tools which underpin all the intuitions in this scenario are hypergraphs and exact set covers. In a rather unexpected, but interesting turn of events, we obtain for free a simple and interesting theorem about the general existence of "rich'' subcontexts. Precisely: every context contains an object/attribute pair which, after removed, results in a context with at least half the original number of concepts.

The thesis examines the comprehensive relationship between all aspects of financial liberalisation and economic growth in three countries from the Economic Community of West African States (ECOWAS). Employing ARDL bounds test approach and real GDP per capita as growth indicator; the thesis finds support in favour of the McKinnon-Shaw hypothesis but also finds that the increases in the subsequent savings and investments have not been transmitted into economic growth in two of the studied countries. Moreover, the thesis also finds that stock market developments have negligible or negative impact on economic growth in two of the selected countries. The thesis concludes that in most cases, it is not financial liberalisation polices that affect economic growth in the selected ECOWAS countries, but rather increase in the productivity of labour, increase in the credit to the private sector, increase in foreign direct investments, increase in the capital stock and increase in government expenditure contrary to expectations. Interestingly, the thesis also finds that export has only negative effect on economic growth in all the selected ECOWAS countries. The thesis therefore, recommends that long-term export diversification programmes be implemented in the ECOWAS regions whilst further investigation is carried on the issue. / Economics / D. Litt et Phil. (Economics)

This study examines the public debt, public debt service and economic growth nexus in Zambia, Zimbabwe and South Africa using time-series data from 1970 to 2017. This research provides empirical evidence to contribute, firstly, to the ongoing public policy debate regarding the dynamic relationship between public debt, public debt service and economic growth, and their causal relationship; and secondly, to the relative impact of domestic and foreign public debt on economic growth in the selected study countries. For this purpose, four empirical models were utilised and estimated using the Autoregressive Distributed Lag (ARDL) bounds to cointegration and the error correction ARDL-based causality test. Model 1 explored the impact of aggregate public debt on economic growth, while Model 2 investigated the relative impact of domestic and foreign public debt on economic growth. Model 3 examined the impact of public debt service on economic growth, whereas the causality between aggregate public debt and economic growth, and between public debt service and economic growth is tested in Model 4a and Model 4b, respectively. Results show that in Model 1, aggregate public debt has a positive impact on economic growth in Zambia but is negative in Zimbabwe and South Africa. In Model 2, domestic public debt negatively impacts economic growth in Zambia and Zimbabwe and positive impact in South Africa. In addition, foreign public debt has a positive impact on economic growth in Zambia and negative impact in Zimbabwe and South Africa. The results from Model 3 largely support a negative relationship between public debt service and economic growth in Zambia and Zimbabwe, and an insignificant relationship in South Africa. The causality results for Model 4a indicate that it is economic growth that drives public debt in all the study countries. Finally, no causal relationship between public debt service and economic growth was confirmed in all the study countries (Model 4b). / Economics / D. Phil. (Economics)