Euler-lagrange equation for a delay variational problem

We establish Euler-Lagrange equations for a problem of Calculus of variations where the unknown variable contains a term of delay on a segment

Optimal portfolio selection with transaction costs

Le choix de portefeuille optimal d'actifs a été depuis longtemps et continue d'être un sujet d'intérêt majeur dans le domaine de la finance. L'objectif principal étant de trouver la meilleure façon d'allouer les ressources financières dans un ensemble d'actifs disponibles sur le marché financier afin de réduire les risques de fluctuation du portefeuille et d'atteindre des rendements élevés. Néanmoins, la littérature de choix de portefeuille a connu une avancée considérable à partir du 20ieme siècle avec l'apparition de nombreuses stratégies motivées essentiellement par le travail pionnier de Markowitz (1952) qui offre une base solide à l'analyse de portefeuille sur le marché financier. Cette thèse, divisée en trois chapitres, contribue à cette vaste littérature en proposant divers outils économétriques pour améliorer le processus de sélection de portefeuilles sur le marché financier afin d'aider les intervenants de ce marché. Le premier chapitre, qui est un papier joint avec Marine Carrasco, aborde un problème de sélection de portefeuille avec coûts de transaction sur le marché financier. Plus précisément, nous développons une procédure de test simple basée sur une estimation de type GMM pour évaluer l'effet des coûts de transaction dans l'économie, quelle que soit la forme présumée des coûts de transaction dans le modèle. En fait, la plupart des études dans la littérature sur l'effet des coûts de transaction dépendent largement de la forme supposée pour ces frictions dans le modèle comme cela a été montré à travers de nombreuses études (Dumas and Luciano (1991), Lynch and Balduzzi (1999), Lynch and Balduzzi (2000), Liu and Loewenstein (2002), Liu (2004), Lesmond et al. (2004), Buss et al. (2011), Gârleanu and Pedersen (2013), Heaton and Lucas (1996)). Ainsi, pour résoudre ce problème, nous développons une procédure statistique, dont le résultat est indépendant de la forme des coûts de transaction, pour tester la significativité de ces coûts dans le processus d'investissement sur le marché financier. Cette procédure de test repose sur l'hypothèse que le modèle estimé par la méthode des moments généralisés (GMM) est correctement spécifié. Un test commun utilisé pour évaluer cette hypothèse est le J-test proposé par Hansen (1982). Cependant, lorsque le paramètre d'intérêt se trouve au bord de l'espace paramétrique, le J-test standard souffre d'un rejet excessif. De ce fait, nous proposons une procédure en deux étapes pour tester la sur-identification lorsque le paramètre d'intérêt est au bord de l'espace paramétrique. Empiriquement, nous appliquons nos procédures de test à la classe des anomalies utilisées par Novy-Marx and Velikov (2016). Nous montrons que les coûts de transaction ont un effet significatif sur le comportement des investisseurs pour la plupart de ces anomalies. Par conséquent, les investisseurs améliorent considérablement les performances hors échantillon en tenant compte des coûts de transaction dans le processus d'investissement. Le deuxième chapitre aborde un problème dynamique de sélection de portefeuille de grande taille. Avec une fonction d'utilité exponentielle, la solution optimale se révèle être une fonction de l'inverse de la matrice de covariance des rendements des actifs. Cependant, lorsque le nombre d'actifs augmente, cet inverse devient peu fiable, générant ainsi une solution qui s'éloigne du portefeuille optimal avec de mauvaises performances. Nous proposons deux solutions à ce problème. Premièrement, nous pénalisons la norme des poids du portefeuille optimal dans le problème dynamique et montrons que la stratégie sélectionnée est asymptotiquement efficace. Cependant, cette méthode contrôle seulement en partie l'erreur d'estimation dans la solution optimale car elle ignore l'erreur d'estimation du rendement moyen des actifs, qui peut également être importante lorsque le nombre d'actifs sur le marché financier augmente considérablement. Nous proposons une méthode alternative qui consiste à pénaliser la norme de la différence de pondérations successives du portefeuille dans le problème dynamique pour garantir que la composition optimale du portefeuille ne fluctue pas énormément entre les périodes. Nous montrons que, sous des conditions de régularité appropriées, nous maîtrisons mieux l'erreur d'estimation dans le portefeuille optimal avec cette nouvelle procédure. Cette deuxième méthode aide les investisseurs à éviter des coûts de transaction élevés sur le marché financier en sélectionnant des stratégies stables dans le temps. Des simulations ainsi qu'une analyse empirique confirment que nos procédures améliorent considérablement la performance du portefeuille dynamique. Dans le troisième chapitre, nous utilisons différentes techniques de régularisation (ou stabilisation) empruntées à la littérature sur les problèmes inverses pour estimer le portefeuille diversifié tel que définie par Choueifaty (2011). En effet, le portefeuille diversifié dépend du vecteur de volatilité des actifs et de l'inverse de la matrice de covariance du rendement des actifs. En pratique, ces deux quantités doivent être remplacées par leurs contrepartie empirique. Cela génère une erreur d'estimation amplifiée par le fait que la matrice de covariance empirique est proche d'une matrice singulière pour un portefeuille de grande taille, dégradant ainsi les performances du portefeuille sélectionné. Pour résoudre ce problème, nous étudions trois techniques de régularisation, qui sont les plus utilisées : le rigde qui consiste à ajouter une matrice diagonale à la matrice de covariance, la coupure spectrale qui consiste à exclure les vecteurs propres associés aux plus petites valeurs propres, et Landweber Fridman qui est une méthode itérative, pour stabiliser l'inverse de matrice de covariance dans le processus d'estimation du portefeuille diversifié. Ces méthodes de régularisation impliquent un paramètre de régularisation qui doit être choisi. Nous proposons donc une méthode basée sur les données pour sélectionner le paramètre de stabilisation de manière optimale. Les solutions obtenues sont comparées à plusieurs stratégies telles que le portefeuille le plus diversifié, le portefeuille cible, le portefeuille de variance minimale et la stratégie naïve 1 / N à l'aide du ratio de Sharpe dans l'échantillon et hors échantillon.The optimal portfolio selection problem has been and continues to be a subject of interest in finance. The main objective is to find the best way to allocate the financial resources in a set of assets available on the financial market in order to reduce the portfolio fluctuation risks and achieve high returns. Nonetheless, there has been a strong advance in the literature of the optimal allocation of financial resources since the 20th century with the proposal of several strategies for portfolio selection essentially motivated by the pioneering work of Markowitz (1952)which provides a solid basis for portfolio analysis on the financial market. This thesis, divided into three chapters, contributes to this vast literature by proposing various economic tools to improve the process of selecting portfolios on the financial market in order to help stakeholders in this market. The first chapter, a joint paper with Marine Carrasco, addresses a portfolio selection problem with trading costs on stock market. More precisely, we develop a simple GMM-based test procedure to test the significance of trading costs effect in the economy regardless of the form of the transaction cost. In fact, most of the studies in the literature about trading costs effect depend largely on the form of the frictions assumed in the model (Dumas and Luciano (1991), Lynch and Balduzzi (1999), Lynch and Balduzzi (2000), Liu and Loewenstein (2002), Liu (2004), Lesmond et al. (2004), Buss et al. (2011), Gârleanu and Pedersen (2013), Heaton and Lucas (1996)). To overcome this problem, we develop a simple test procedure which allows us to test the significance of trading costs effect on a given asset in the economy without any assumption about the form of these frictions. Our test procedure relies on the assumption that the model estimated by GMM is correctly specified. A common test used to evaluate this assumption is the standard J-test proposed by Hansen (1982). However, when the true parameter is close to the boundary of the parameter space, the standard J-test based on the chi2 critical value suffers from overrejection. To overcome this problem, we propose a two-step procedure to test overidentifying restrictions when the parameter of interest approaches the boundary of the parameter space. In an empirical analysis, we apply our test procedures to the class of anomalies used in Novy-Marx and Velikov (2016). We show that transaction costs have a significant effect on investors' behavior for most anomalies. In that case, investors significantly improve out-of-sample performance by accounting for trading costs. The second chapter addresses a multi-period portfolio selection problem when the number of assets in the financial market is large. Using an exponential utility function, the optimal solution is shown to be a function of the inverse of the covariance matrix of asset returns. Nonetheless, when the number of assets grows, this inverse becomes unreliable, yielding a selected portfolio that is far from the optimal one. We propose two solutions to this problem. First, we penalize the norm of the portfolio weights in the dynamic problem and show that the selected strategy is asymptotically efficient. However, this method partially controls the estimation error in the optimal solution because it ignores the estimation error in the expected return, which may also be important when the number of assets in the financial market increases considerably. We propose an alternative method that consists of penalizing the norm of the difference of successive portfolio weights in the dynamic problem to guarantee that the optimal portfolio composition does not fluctuate widely between periods. We show, under appropriate regularity conditions, that we better control the estimation error in the optimal portfolio with this new procedure. This second method helps investors to avoid high trading costs in the financial market by selecting stable strategies over time. Extensive simulations and empirical results confirm that our procedures considerably improve the performance of the dynamic portfolio. In the third chapter, we use various regularization (or stabilization) techniques borrowed from the literature on inverse problems to estimate the maximum diversification as defined by Choueifaty (2011). In fact, the maximum diversification portfolio depends on the vector of asset volatilities and the inverse of the covariance matrix of assets distribution. In practice, these two quantities need to be replaced by their sample counterparts. This results in estimation error which is amplified by the fact that the sample covariance matrix may be close to a singular matrix in a large financial market, yielding a selected portfolio far from the optimal one with very poor performance. To address this problem, we investigate three regularization techniques, such as the ridge, the spectral cut-off, and the Landweber-Fridman, to stabilize the inverse of the covariance matrix in the investment process. These regularization schemes involve a tuning parameter that needs to be chosen. So, we propose a data-driven method for selecting the tuning parameter in an optimal way. The resulting regularized rules are compared to several strategies such as the most diversified portfolio, the target portfolio, the global minimum variance portfolio, and the naive 1/N strategy in terms of in-sample and out-of-sample Sharpe ratio

Measuring female factor in determinants of entrepreneurship: illustration by case of Côte d\u27Ivoire through a quasi-experimental ex-post approach

Purpose of this article is to find out whether determinants of women entrepreneurship are different from those of men’s entrepreneurship in general and specifically in Côte d’Ivoire. To do this, we conducted a quasi-experimental analysis using non-parametric and parametric approaches to survey data on a sample of 161 entrepreneurs in Côte d\u27Ivoire, 113 of whom were women and 48 men. Our survey was designed and conducted to neutralize the socio-demographic and conjunctural differences between men and women entrepreneurship in order to produce matched data. Our analysis shows that determinants of male and female entrepreneurship in Côte d\u27Ivoire are not fundamentally different if rationality matters

The Impact of Performance-Based Assessment on University ESL Learners\u27 Motivation

This thesis examines the impact of performance-based assessment on university ESL learners\u27 motivation. To reach this aim, data were collected from 21 international ESL students taking an intensive oracy course for non-native speakers. Online motivation questionnaires were used in order to find out how these learners responded emotionally and motivationally to performance-based assessment, specifically an oral presentation project both before and after the project. The results revealed that the students responded positively to this type of project. However, their motivational and emotional states varied across time depending on their experience with the oral presentation, their performance, and the cohesion of their group

Treatment seeking, access to care and child health: Evidence from the Taabo health and demographic surveillance site (HDSS) in Côte d’Ivoire

Background: Despite substantial progress over the last two decades, under-five mortality remains high in many African settings. Current estimates suggest that Sustainable Development Goal 3.2 of reducing under-5 mortality (U5MR) to levels below 25 deaths per 1000 live births by 2030 will not be achieved in sub-Saharan Africa. In countries with high under-five mortality, further improvements in child mortality will only be possible if essential health services become available and accessible for those most in need. Access is a complex concept. Even if there is easy access to health facilities and an adequate supply of services, the extent to which specific populations access these services depends on the livelihood of the household, the community, and the wider society. Half of all under-five deaths are neonatal deaths many of which could be prevented through improved antenatal care (ANC). Access to adequate health care in remote areas, including prenatal and post-natal health services, as well as delayed attendance of health facilities have been identified as key determinants of the continued high burden of under-five mortality in these settings. Child mortality and its underlying factors vary substantially across and within countries. Thus, a local understanding of under-five mortality and its relation with treatment seeking and access to care is important in the development of local sustainable intervention strategies aiming to reduce the continued high burden of under-five mortality. Goal and specific objectives: The overall objective of this PhD project was to identify effective ways to improve health service access and child health in low and middle-income country settings in general, and in the Taabo health and demographic surveillance system (HDSS) in Côte d’Ivoire in particular. To address this general objective, we pursued three specific aims. First, we aimed to identify the most critical household and community characteristics influencing treatment seeking for under-five children. Second, we assessed whether the construction of additional health facilities can improve treatment seeking and child health outcomes. Third, we assessed whether access to essential antenatal services as well as maternal and child health can be improved through community programmes. Methods: The thesis pursued three complementary approaches to address key challenges in health care access and delivery. For the first aim, we used prospectively collected data from 736 non-fatal and 82 fatal cases reports of under-five children during the year 2017 from the Taabo HDSS. Caregivers of children with a recent non-fatal illness episode residing in the Taabo health district, south-central Côte d’Ivoire were interviewed using a social autopsy questionnaire. For the second aim, we used detailed demographic surveillance data obtained from the Taabo HDSS. Since 2009, the Taabo HDSS has been continuously monitoring a population of over 40,000 inhabitants by reporting vital events such as pregnancies, births, deaths, and migration through surveillance rounds. We used panel data from the HDSS covering all children under age five born in the HDSS between 2010 and 2018. Between 2010 and 2018, four new health facilities were constructed within the Taabo HDSS area with the ambition to reduce distance and travel times to health facilities, and ultimately to improve health outcomes. We conducted a quasi-experimental study assessing the impact of newly constructed facilities. For the third aim, we conducted a three-arm cluster Randomized Control Trial (cRCT) to assess the effectiveness of two complementary strategies in increasing iron and folic acid supplementation and malaria chemoprophylaxis coverage among pregnant women. We randomly assigned 39 clusters to the control group, 39 clusters to the information group, and 40 clusters to the information plus home delivery of iron and folic acid (IFA) supplements group. Trial participants were pregnant women who were at least 15 years old and in their first or second trimester. The interventions consisted of an information package, designed to increase uptake of essential antenatal services through targeted information, and an information plus home delivery intervention, designed to provide both information and immediate access to supplements and chemoprophylaxis. Through an end line survey within the first two weeks after delivery, we assessed the relative effectiveness of each intervention. Results: In this primarily rural part of Côte d’Ivoire, treatment seeking was largely directed towards modern medicine. In non-fatal cases, modern treatment seeking was associated with child-specific factors (age, relationship with caregiver), caregiver education, and household proximity to the nearest health facility as well as clinical signs such as fever, severe vomiting, inability to drink, convulsion, and inability to play. In fatal cases, modern healthcare was sought only for signs of lower respiratory disease. The lack of awareness regarding disease-related clinical danger signs were identified as the potential barriers to accessing health care. The results of our quasi-experimental study showed that local provision of new health facilities declined the average distance to the nearest health facility. However, this decline did not improve neonatal survival outcome or maternal health services utilization. Positive impacts were found for post-neonatal infant mortality, which was reduced by 46%. Our intervention trial suggest that community-based programs can improve compliance with IFA supplementation and malaria chemoprophylaxis during pregnancy. High compliance with Sulfadoxine-pyrimethamine (SP) treatment was sufficient to largely remove the risk of malaria infection. Increased compliance with standard IFA supplementation was insufficient to address the high prevalence of postpartum anemia in the study setting. Conclusion: The findings presented here from a primarily rural part of Côte d’Ivoire suggest that a large proportion of caregivers seek modern care for their under 5-year-old children, but that some mild and severe illness cases continue to remain untreated. Interventions promoting prompt healthcare seeking and the recognition of danger signs may help improve treatment seeking in rural settings of Côte d’Ivoire, and can potentially help further reduce under-five mortality. Our study suggests that local construction of new health centers in a mainly rural part of south-central Côte d’Ivoire may have only relatively limited impact on healthcare utilization and overall population health. More research will be needed to better understand the somewhat limited impacts seen in this study as well as to identify the health infrastructure needed more generally for improving health outcomes in this setting. The results from our trial suggest that combining information with direct home delivery of supplements and hemoprophylaxis can increase compliance with IFA supplementation and malaria prevention and reduce the risk of malaria infection. However, more powerful interventions are likely needed to address the high burden of anemia in this population

Family Choices for the Career Woman in the Twenty-First Century

This study poses the question, ls it possible for the twenty-first century woman to successfully integrate career and family, and if so, how? Feminine identity, role, and fulfillment are changing and continue to transform in modern society. Today the twenty-first century woman struggles to integrate career, family, and home successfully while understanding the passion or driving force in her life. This research explores gender roles in order to understand, update, and find order in a chaotic world. Feminist thought and chaos theory are examined to see whether or not it is possible to integrate family and career in the new millennium, what prevents integration, and what is needed for integration to be successful. The women\u27s movement, scholarly articles, and modem case studies are explored in this study. The answers lie in helping each woman understand her purpose, discover what really matters to her, and then use this information to lead a purposeful life that impacts the world around her