MA167exam01

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

Distribución hiperbólica generalizada: una aplicación en la selección de portafolios y en la cuantificación de medidas de riesgo de mercado

En este trabajo se implementa una metodología para incluir momentos de orden superior en la selección de portafolios, haciendo uso de la Distribución Hiperbólica Generalizada, para posteriormente hacer un análisis comparativo frente al modelo de Markowitz.

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

Measuring and testing for the systemically important financial institutions

This paper analyzes the measure of systemic importance ∆CoV aR proposed by Adrian and Brunnermeier (2009, 2010) within the context of a similar class of risk measures used in the risk management literature. In addition, we develop a series of testing procedures, based on ∆CoV aR, to identify and rank the systemically important institutions. We stress the importance of statistical testing in interpreting the measure of systemic importance. An empirical application illustrates the testing procedures, using equity data for three European banks.

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

MARCKS functions as a novel growth/tumour suppressor in cells of melanocyte origin

Protein kinase C (PKC) plays a pivotal role in modulating the growth of melanocytic cells in culture. We have shown previously that a major physiological substrate of PKC, the 80 kDa myristoylated alanine-rich C-kinase substrate (MARCKS), can be phosphorylated in quiescent, non-tumorigenic melanocytes exposed transiently to a biologically active phorbol ester, but cannot be phosphorylated in phorbol ester-treated, syngeneic malignant melanoma cells. Despite its ubiquitous distribution, the function of MARCKS in cell growth and transformation remains to be demonstrated clearly. We report here that MARCKS mRNA and protein levels are down-regulated significantly in the spontaneously derived murine B16 melanoma cell line compared with syngeneic normal Mel-ab melanocytes. In contrast, the tumourigenic v-Ha-ras-transfonned melan-ocytic line, LTR Ras 2, showed a high basal level of MARCKS phosphorylation which was not enhanced by treatment of cells with phorbol ester. Furthermore, protein levels of MARCKS in LTR Ras 2 cells were similar to those expressed in Mel-ab melanocytes. However, in four out of six murine tumour cell lines investigated, levels of MARCKS protein were barely detectable. Transfection of B16 cells with a plasmid containing the MARCKS cDNA in the sense orientation produced two neomycin-resistant clones displaying reduced proliferative capacity and decreased anchorage-independent growth compared with control cells. In contrast, transfection with the antisense MARCKS construct produced many colonies which displayed enhanced growth and transforming potential compared with control cells. Thus, MARCKS appears to act as a novel growth suppressor in the spontaneous transformation of cells of melanocyte origin and may play a more general role in the tumour progression of other carcinomas.

The spatial distribution of carbon dioxide in an environmental test chamber

The spatial distribution of CO2 level in a classroom carried out in previous field work research has demonstrated that there is some evidence of variations in CO2 concentration in a classroom space. Significant fluctuations in CO2 concentration were found at different sampling points depending on the ventilation strategies and environmental conditions prevailing in individual classrooms. However, how these variations are affected by the emitting sources and the room air movement remains unknown. Hence, it was concluded that detailed investigation of the CO2 distribution need to be performed on a smaller scale. As a result, it was decided to use an environmental chamber with various methods and rates of ventilation, for the same internal temperature and heat loads, to study the effect of ventilation strategy and air movement on the distribution of CO2 concentration in a room. The role of human exhalation and its interaction with the plume induced by the body's convective flow and room air movement due to different ventilation strategies were studied in a chamber at the University of Reading. These phenomena are considered to be important in understanding and predicting the flow patterns in a space and how these impact on the distribution of contaminants. This paper attempts to study the CO2 dispersion and distribution at the exhalation zone of two people sitting in a chamber as well as throughout the occupied zone of the chamber. The horizontal and vertical distributions of CO2 were sampled at locations with a probability that CO2 variation is considered high. Although the room size, source location, ventilation rate and location of air supply and extract devices all can have influence on the CO2 distribution, this article gives general guidelines on the optimum positioning of CO2 sensor in a room.

A new study on the power distribution of OFDMA, SC-FDMA and CP-CDMA signals

This paper explores a new technique to calculate and plot the distribution of instantaneous transmit envelope power of OFDMA and SC-FDMA signals from the equation of Probability Density Function (PDF) solved numerically. The Complementary Cumulative Distribution Function (CCDF) of Instantaneous Power to Average Power Ratio (IPAPR) is computed from the structure of the transmit system matrix. This helps intuitively understand the distribution of output signal power if the structure of the transmit system matrix and the constellation used are known. The distribution obtained for OFDMA signal matches complex normal distribution. The results indicate why the CCDF of IPAPR in case of SC-FDMA is better than OFDMA for a given constellation. Finally, with this method it is shown again that cyclic prefixed DS-CDMA system is one case with optimum IPAPR. The insight that this technique provides may be useful in designing area optimised digital and power efficient analogue modules.

Asymptotic expansions for Taylor coefficients of the composition of two functions

We give an asymptotic expansion for the Taylor coe±cients of L(P(z)) where L(z) is analytic in the open unit disc whose Taylor coe±cients vary `smoothly' and P(z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences.

Smoothness of scale functions for spectrally negative Lévy processes

Scale functions play a central role in the fluctuation theory of spectrally negative Lévy processes and often appear in the context of martingale relations. These relations are often require excursion theory rather than Itô calculus. The reason for the latter is that standard Itô calculus is only applicable to functions with a sufficient degree of smoothness and knowledge of the precise degree of smoothness of scale functions is seemingly incomplete. The aim of this article is to offer new results concerning properties of scale functions in relation to the smoothness of the underlying Lévy measure. We place particular emphasis on spectrally negative Lévy processes with a Gaussian component and processes of bounded variation. An additional motivation is the very intimate relation of scale functions to renewal functions of subordinators. The results obtained for scale functions have direct implications offering new results concerning the smoothness of such renewal functions for which there seems to be very little existing literature on this topic.

A unified neurofuzzy model for classification

This work proposes a unified neurofuzzy modelling scheme. To begin with, the initial fuzzy base construction method is based on fuzzy clustering utilising a Gaussian mixture model (GMM) combined with the analysis of covariance (ANOVA) decomposition in order to obtain more compact univariate and bivariate membership functions over the subspaces of the input features. The mean and covariance of the Gaussian membership functions are found by the expectation maximisation (EM) algorithm with the merit of revealing the underlying density distribution of system inputs. The resultant set of membership functions forms the basis of the generalised fuzzy model (GFM) inference engine. The model structure and parameters of this neurofuzzy model are identified via the supervised subspace orthogonal least square (OLS) learning. Finally, instead of providing deterministic class label as model output by convention, a logistic regression model is applied to present the classifier’s output, in which the sigmoid type of logistic transfer function scales the outputs of the neurofuzzy model to the class probability. Experimental validation results are presented to demonstrate the effectiveness of the proposed neurofuzzy modelling scheme.

Species distribution models for crop pollination: a modelling framework applied to Great Britain

Insect pollination benefits over three quarters of the world's major crops. There is growing concern that observed declines in pollinators may impact on production and revenues from animal pollinated crops. Knowing the distribution of pollinators is therefore crucial for estimating their availability to pollinate crops; however, in general, we have an incomplete knowledge of where these pollinators occur. We propose a method to predict geographical patterns of pollination service to crops, novel in two elements: the use of pollinator records rather than expert knowledge to predict pollinator occurrence, and the inclusion of the managed pollinator supply. We integrated a maximum entropy species distribution model (SDM) with an existing pollination service model (PSM) to derive the availability of pollinators for crop pollination. We used nation-wide records of wild and managed pollinators (honey bees) as well as agricultural data from Great Britain. We first calibrated the SDM on a representative sample of bee and hoverfly crop pollinator species, evaluating the effects of different settings on model performance and on its capacity to identify the most important predictors. The importance of the different predictors was better resolved by SDM derived from simpler functions, with consistent results for bees and hoverflies. We then used the species distributions from the calibrated model to predict pollination service of wild and managed pollinators, using field beans as a test case. The PSM allowed us to spatially characterize the contribution of wild and managed pollinators and also identify areas potentially vulnerable to low pollination service provision, which can help direct local scale interventions. This approach can be extended to investigate geographical mismatches between crop pollination demand and the availability of pollinators, resulting from environmental change or policy scenarios.

Occurrence probability, width and number of steps of cusp precipitation for fully pulsed reconnection at the dayside magnetopause

We discuss the characteristics of magnetosheath plasma precipitation in the “cusp” ionosphere for when the reconnection at the dayside magnetopause takes place only in a series of pulses. It is shown that even in this special case, the low-altitude cusp precipitation is continuous, unless the intervals between the pulses are longer than observed intervals between magnetopause flux transfer event (FTE) signatures. We use FTE observation statistics to predict, for this case of entirely pulsed reconnection, the occurrence frequency, the distribution of latitudinal widths, and the number of ion dispersion steps of the cusp precipitation for a variety of locations of the reconnection site and a range of values of the local de-Hoffman Teller velocity. It is found that the cusp occurrence frequency is comparable with observed values for virtually all possible locations of the reconnection site. The distribution of cusp width is also comparable with observations and is shown to be largely dependent on the distribution of the mean reconnection rate, but pulsing the reconnection does very slightly increase the width of that distribution compared with the steady state case. We conclude that neither cusp occurrence probability nor width can be used to evaluate the relative occurrence of reconnection behaviors that are entirely pulsed, pulsed but continuous and quasi-steady. We show that the best test of the relative frequency of these three types of reconnection is to survey the distribution of steps in the cusp ion dispersion characteristics.

Improving the estimation of probability of bidder participation in procurement auctions

Anticipating the number and identity of bidders has significant influence in many theoretical results of the auction itself and bidders' bidding behaviour. This is because when a bidder knows in advance which specific bidders are likely competitors, this knowledge gives a company a head start when setting the bid price. However, despite these competitive implications, most previous studies have focused almost entirely on forecasting the number of bidders and only a few authors have dealt with the identity dimension qualitatively. Using a case study with immediate real-life applications, this paper develops a method for estimating every potential bidder's probability of participating in a future auction as a function of the tender economic size removing the bias caused by the contract size opportunities distribution. This way, a bidder or auctioner will be able to estimate the likelihood of a specific group of key, previously identified bidders in a future tender.

Cosmic shear requirements on the wavelength dependence of telescope point spread functions

Cosmic shear requires high precision measurement of galaxy shapes in the presence of the observational point spread function (PSF) that smears out the image. The PSF must therefore be known for each galaxy to a high accuracy. However, for several reasons, the PSF is usually wavelength dependent; therefore, the differences between the spectral energy distribution of the observed objects introduce further complexity. In this paper, we investigate the effect of the wavelength dependence of the PSF, focusing on instruments in which the PSF size is dominated by the diffraction limit of the telescope and which use broad-band filters for shape measurement. We first calculate biases on cosmological parameter estimation from cosmic shear when the stellar PSF is used uncorrected. Using realistic galaxy and star spectral energy distributions and populations and a simple three-component circular PSF, we find that the colour dependence must be taken into account for the next generation of telescopes. We then consider two different methods for removing the effect: (i) the use of stars of the same colour as the galaxies and (ii) estimation of the galaxy spectral energy distribution using multiple colours and using a telescope model for the PSF. We find that both of these methods correct the effect to levels below the tolerances required for per cent level measurements of dark energy parameters. Comparison of the two methods favours the template-fitting method because its efficiency is less dependent on galaxy redshift than the broad-band colour method and takes full advantage of deeper photometry.