The mean-variance model from the inverse of the variance-covariance matrix

En este artículo, a partir de la inversa de la matriz de varianzas y covarianzas se obtiene el modelo Esperanza-Varianza de Markowitz siguiendo un camino más corto y matemáticamente riguroso. También se obtiene la ecuación de equilibrio del CAPM de Sharpe.

Buy-and-Hold Strategies and Comonotonic Approximations

[cat] En aquest article estudiem estratègies “comprar i mantenir” per a problemes d’optimitzar la riquesa final en un context multi-període. Com que la riquesa final és una suma de variables aleatòries dependents, on cadascuna d’aquestes correspon a una quantitat de capital que s’ha invertit en un actiu particular en una data determinada, en primer lloc considerem aproximacions que redueixen l’aleatorietat multivariant al cas univariant. A continuació, aquestes aproximacions es fan servir per determinar les estratègies “comprar i mantenir” que optimitzen, per a un nivell de probabilitat donat, el VaR i el CLTE de la funció de distribució de la riquesa final. Aquest article complementa el treball de Dhaene et al. (2005), on es van considerar estratègies de reequilibri constant.

Complements and substitutes in multilateral assignment markets

[cat] En aquest treball provo que, en mercats d’assignació amb més de dos costats, agents de diferents sectors poden no ser complementaris mentre que agents del mateix sector poden no ser substituts. Shapley (1962) va provar que això mai pot succeïr quan el mercat d’assignació només té dos costats. No obstant, demostro que existeixen condicions suficients que garanteixen la substitutabilitat i la complementarietat entre agents en aquests tipus de mercats. A més, provo que, quan els béns al mercat son homogenis, el resultat de Shapley (1962) es manté.

Optimal fiscal policy in overlapping generations models

[eng] This paper provides, from a theoretical and quantitative point of view, an explanation of why taxes on capital returns are high (around 35%) by analyzing the optimal fiscal policy in an economy with intergenerational redistribution. For this purpose, the government is modeled explicitly and can choose (and commit to) an optimal tax policy in order to maximize society's welfare. In an infinitely lived economy with heterogeneous agents, the long run optimal capital tax is zero. If heterogeneity is due to the existence of overlapping generations, this result in general is no longer true. I provide sufficient conditions for zero capital and labor taxes, and show that a general class of preferences, commonly used on the macro and public finance literature, violate these conditions. For a version of the model, calibrated to the US economy, the main results are: first, if the government is restricted to a set of instruments, the observed fiscal policy cannot be disregarded as sub optimal and capital taxes are positive and quantitatively relevant. Second, if the government can use age specific taxes for each generation, then the age profile capital tax pattern implies subsidizing asset returns of the younger generations and taxing at higher rates the asset returns of the older ones.

Essays on the treatment of cash flows under stochastic interest rates

Abstract This paper shows how to calculate recursively the moments of the accumulated and discounted value of cash flows when the instantaneous rates of return follow a conditional ARMA process with normally distributed innovations. We investigate various moment based approaches to approximate the distribution of the accumulated value of cash flows and we assess their performance through stochastic Monte-Carlo simulations. We discuss the potential use in insurance and especially in the context of Asset-Liability Management of pension funds.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Midwest Transportation Consortium Annual Report, 2004-2005

The Midwest Transportation Consortium (MTC) recently completed its sixth year of operation. The MTC has become an established portion of the research and educational programs at ISU and its partner universities. The MTC continues to emphasize its primary focus of developing human capital. For example, this semester, Fall, 2005, ISU has graduate scholars in its educational program. However, we also recognize that the federal grant is an opportunity to build programs at our respective universities that continue after the U.S. DOT UTCP may end. An example of building a long lasting program is the University of Missouri – St. Louis’ (UMSL) and its development of a transportation Ph.D. program in their business college. Admittedly, this program could have been started regardless, but Dr. Ray Mundy, Director of UMSL’s Transportation Scholars Program, believes that the MTC support of the transportation educational program at UMSL was the essential component in establishing a Ph.D. program. At ISU, the MTC has been instrumental in establishing two research and outreach programs, and both have themes that are related to the MTC’s theme of “Transportation System Management and Operation.” The Center for Weather Impacts on Mobility and Safety (C-WIMS) was recently established, and the Center for Road Infrastructure Management and Operations (RIMO) is in the process of being established. The MTC has a critical role in establishing each of these two programs. As part of the on-going MTC program, we have established an effective network that promotes the education of future transportation professionals and the development of new knowledge on how to manage transportation infrastructure and services in a more sustainable manner. The MTC has a track record of developing outstanding students; these students are now becoming leaders in the private sector, government, and academia. The MTC has also supported the development of an extensive research portfolio related to sustainable transportation asset management. More research projects are in the pipeline. Finally, the MTC has dedicated itself to the dissemination of asset management research results through an ongoing technology transfer program. This document provides a progress for the latest fiscal year of operation of the MTC, which ran from October 2004 through September 2005.

Midwest Transportation Consortium Annual Report, 2005-2006

The Midwest Transportation Consortium (MTC) recently completed its sixth year of operation. The MTC has become an established portion of the research and educational programs at ISU and its partner universities. The MTC continues to emphasize its primary focus of developing human capital. For example, this semester, Fall, 2005, ISU has graduate scholars in its educational program. However, we also recognize that the federal grant is an opportunity to build programs at our respective universities that continue after the U.S. DOT UTCP may end. An example of building a long lasting program is the University of Missouri – St. Louis’ (UMSL) and its development of a transportation Ph.D. program in their business college. Admittedly, this program could have been started regardless, but Dr. Ray Mundy, Director of UMSL’s Transportation Scholars Program, believes that the MTC support of the transportation educational program at UMSL was the essential component in establishing a Ph.D. program. At ISU, the MTC has been instrumental in establishing two research and outreach programs, and both have themes that are related to the MTC’s theme of “Transportation System Management and Operation.” The Center for Weather Impacts on Mobility and Safety (C-WIMS) was recently established, and the Center for Road Infrastructure Management and Operations (RIMO) is in the process of being established. The MTC has a critical role in establishing each of these two programs. As part of the on-going MTC program, we have established an effective network that promotes the education of future transportation professionals and the development of new knowledge on how to manage transportation infrastructure and services in a more sustainable manner. The MTC has a track record of developing outstanding students; these students are now becoming leaders in the private sector, government, and academia. The MTC has also supported the development of an extensive research portfolio related to sustainable transportation asset management. More research projects are in the pipeline. Finally, the MTC has dedicated itself to the dissemination of asset management research results through an ongoing technology transfer program. This document provides a progress for the latest fiscal year of operation of the MTC, which ran from October 2004 through September 2005.

Midwest Transportation Consortium Annual Report, 2006-2007

The Midwest Transportation Consortium (MTC) recently completed its sixth year of operation. The MTC has become an established portion of the research and educational programs at ISU and its partner universities. The MTC continues to emphasize its primary focus of developing human capital. For example, this semester, Fall, 2005, ISU has graduate scholars in its educational program. However, we also recognize that the federal grant is an opportunity to build programs at our respective universities that continue after the U.S. DOT UTCP may end. An example of building a long lasting program is the University of Missouri – St. Louis’ (UMSL) and its development of a transportation Ph.D. program in their business college. Admittedly, this program could have been started regardless, but Dr. Ray Mundy, Director of UMSL’s Transportation Scholars Program, believes that the MTC support of the transportation educational program at UMSL was the essential component in establishing a Ph.D. program. At ISU, the MTC has been instrumental in establishing two research and outreach programs, and both have themes that are related to the MTC’s theme of “Transportation System Management and Operation.” The Center for Weather Impacts on Mobility and Safety (C-WIMS) was recently established, and the Center for Road Infrastructure Management and Operations (RIMO) is in the process of being established. The MTC has a critical role in establishing each of these two programs. As part of the on-going MTC program, we have established an effective network that promotes the education of future transportation professionals and the development of new knowledge on how to manage transportation infrastructure and services in a more sustainable manner. The MTC has a track record of developing outstanding students; these students are now becoming leaders in the private sector, government, and academia. The MTC has also supported the development of an extensive research portfolio related to sustainable transportation asset management. More research projects are in the pipeline. Finally, the MTC has dedicated itself to the dissemination of asset management research results through an ongoing technology transfer program. This document provides a progress for the latest fiscal year of operation of the MTC, which ran from October 2004 through September 2005.

Midwest Transportation Consortium Annual Report, 2007-2008

The Midwest Transportation Consortium (MTC) recently completed its sixth year of operation. The MTC has become an established portion of the research and educational programs at ISU and its partner universities. The MTC continues to emphasize its primary focus of developing human capital. For example, this semester, Fall, 2005, ISU has graduate scholars in its educational program. However, we also recognize that the federal grant is an opportunity to build programs at our respective universities that continue after the U.S. DOT UTCP may end. An example of building a long lasting program is the University of Missouri – St. Louis’ (UMSL) and its development of a transportation Ph.D. program in their business college. Admittedly, this program could have been started regardless, but Dr. Ray Mundy, Director of UMSL’s Transportation Scholars Program, believes that the MTC support of the transportation educational program at UMSL was the essential component in establishing a Ph.D. program. At ISU, the MTC has been instrumental in establishing two research and outreach programs, and both have themes that are related to the MTC’s theme of “Transportation System Management and Operation.” The Center for Weather Impacts on Mobility and Safety (C-WIMS) was recently established, and the Center for Road Infrastructure Management and Operations (RIMO) is in the process of being established. The MTC has a critical role in establishing each of these two programs. As part of the on-going MTC program, we have established an effective network that promotes the education of future transportation professionals and the development of new knowledge on how to manage transportation infrastructure and services in a more sustainable manner. The MTC has a track record of developing outstanding students; these students are now becoming leaders in the private sector, government, and academia. The MTC has also supported the development of an extensive research portfolio related to sustainable transportation asset management. More research projects are in the pipeline. Finally, the MTC has dedicated itself to the dissemination of asset management research results through an ongoing technology transfer program. This document provides a progress for the latest fiscal year of operation of the MTC, which ran from October 2004 through September 2005.

Midwest Transportation Consortium Annual Report, 2009

The Midwest Transportation Consortium (MTC) recently completed its sixth year of operation. The MTC has become an established portion of the research and educational programs at ISU and its partner universities. The MTC continues to emphasize its primary focus of developing human capital. For example, this semester, Fall, 2005, ISU has graduate scholars in its educational program. However, we also recognize that the federal grant is an opportunity to build programs at our respective universities that continue after the U.S. DOT UTCP may end. An example of building a long lasting program is the University of Missouri – St. Louis’ (UMSL) and its development of a transportation Ph.D. program in their business college. Admittedly, this program could have been started regardless, but Dr. Ray Mundy, Director of UMSL’s Transportation Scholars Program, believes that the MTC support of the transportation educational program at UMSL was the essential component in establishing a Ph.D. program. At ISU, the MTC has been instrumental in establishing two research and outreach programs, and both have themes that are related to the MTC’s theme of “Transportation System Management and Operation.” The Center for Weather Impacts on Mobility and Safety (C-WIMS) was recently established, and the Center for Road Infrastructure Management and Operations (RIMO) is in the process of being established. The MTC has a critical role in establishing each of these two programs. As part of the on-going MTC program, we have established an effective network that promotes the education of future transportation professionals and the development of new knowledge on how to manage transportation infrastructure and services in a more sustainable manner. The MTC has a track record of developing outstanding students; these students are now becoming leaders in the private sector, government, and academia. The MTC has also supported the development of an extensive research portfolio related to sustainable transportation asset management. More research projects are in the pipeline. Finally, the MTC has dedicated itself to the dissemination of asset management research results through an ongoing technology transfer program. This document provides a progress for the latest fiscal year of operation of the MTC, which ran from October 2004 through September 2005.

Midwest Transportation Consortium Annual Report, 2010

The Midwest Transportation Consortium (MTC) recently completed its sixth year of operation. The MTC has become an established portion of the research and educational programs at ISU and its partner universities. The MTC continues to emphasize its primary focus of developing human capital. For example, this semester, Fall, 2005, ISU has graduate scholars in its educational program. However, we also recognize that the federal grant is an opportunity to build programs at our respective universities that continue after the U.S. DOT UTCP may end. An example of building a long lasting program is the University of Missouri – St. Louis’ (UMSL) and its development of a transportation Ph.D. program in their business college. Admittedly, this program could have been started regardless, but Dr. Ray Mundy, Director of UMSL’s Transportation Scholars Program, believes that the MTC support of the transportation educational program at UMSL was the essential component in establishing a Ph.D. program. At ISU, the MTC has been instrumental in establishing two research and outreach programs, and both have themes that are related to the MTC’s theme of “Transportation System Management and Operation.” The Center for Weather Impacts on Mobility and Safety (C-WIMS) was recently established, and the Center for Road Infrastructure Management and Operations (RIMO) is in the process of being established. The MTC has a critical role in establishing each of these two programs. As part of the on-going MTC program, we have established an effective network that promotes the education of future transportation professionals and the development of new knowledge on how to manage transportation infrastructure and services in a more sustainable manner. The MTC has a track record of developing outstanding students; these students are now becoming leaders in the private sector, government, and academia. The MTC has also supported the development of an extensive research portfolio related to sustainable transportation asset management. More research projects are in the pipeline. Finally, the MTC has dedicated itself to the dissemination of asset management research results through an ongoing technology transfer program. This document provides a progress for the latest fiscal year of operation of the MTC, which ran from October 2004 through September 2005.

Midwest Transportation Consortium Annual Report, 2011

The Midwest Transportation Consortium (MTC) recently completed its sixth year of operation. The MTC has become an established portion of the research and educational programs at ISU and its partner universities. The MTC continues to emphasize its primary focus of developing human capital. For example, this semester, Fall, 2005, ISU has graduate scholars in its educational program. However, we also recognize that the federal grant is an opportunity to build programs at our respective universities that continue after the U.S. DOT UTCP may end. An example of building a long lasting program is the University of Missouri – St. Louis’ (UMSL) and its development of a transportation Ph.D. program in their business college. Admittedly, this program could have been started regardless, but Dr. Ray Mundy, Director of UMSL’s Transportation Scholars Program, believes that the MTC support of the transportation educational program at UMSL was the essential component in establishing a Ph.D. program. At ISU, the MTC has been instrumental in establishing two research and outreach programs, and both have themes that are related to the MTC’s theme of “Transportation System Management and Operation.” The Center for Weather Impacts on Mobility and Safety (C-WIMS) was recently established, and the Center for Road Infrastructure Management and Operations (RIMO) is in the process of being established. The MTC has a critical role in establishing each of these two programs. As part of the on-going MTC program, we have established an effective network that promotes the education of future transportation professionals and the development of new knowledge on how to manage transportation infrastructure and services in a more sustainable manner. The MTC has a track record of developing outstanding students; these students are now becoming leaders in the private sector, government, and academia. The MTC has also supported the development of an extensive research portfolio related to sustainable transportation asset management. More research projects are in the pipeline. Finally, the MTC has dedicated itself to the dissemination of asset management research results through an ongoing technology transfer program. This document provides a progress for the latest fiscal year of operation of the MTC, which ran from October 2004 through September 2005.

Media, investors and bubbles

We analysed the specific case of how information in the financial press influences economic bubbles. We found considerable flaws in the information market due to several factors: demand, the predominance of what are termed “irrational investors” (herding), and supply, which has the problem that the sources of information are biasedand feeds. A financial bubble is a deviation between real value of a financial asset and its persistent market price in time, which also has a speculative origin fed back by the illusion of the owners of these financial values, who will take benefits because of the future prices, which must be higher than the previous ones. The economical information in the media is submitting three problems. First of all, it is information generated by companies. In second place, the information circuit is fed back. A problem of informative independence becomes created, particularly serious in the case of the banks, which are very were as creditors. And in a third place, some informative biases are manifested for the companies of regulated sectors which are starring the economical information in the media.

SA2RAGE: a new sequence for fast B1+ -mapping.

At high magnetic field strengths (≥ 3T), the radiofrequency wavelength used in MRI is of the same order of magnitude of (or smaller than) the typical sample size, making transmit magnetic field (B1+) inhomogeneities more prominent. Methods such as radiofrequency-shimming and transmit SENSE have been proposed to mitigate these undesirable effects. A prerequisite for such approaches is an accurate and rapid characterization of the B1+ field in the organ of interest. In this work, a new phase-sensitive three-dimensional B1+-mapping technique is introduced that allows the acquisition of a 64 × 64 × 8 B1+-map in ≈ 20 s, yielding an accurate mapping of the relative B1+ with a 10-fold dynamic range (0.2-2 times the nominal B1+). Moreover, the predominant use of low flip angle excitations in the presented sequence minimizes specific absorption rate, which is an important asset for in vivo B1+-shimming procedures at high magnetic fields. The proposed methodology was validated in phantom experiments and demonstrated good results in phantom and human B1+-shimming using an 8-channel transmit-receive array.