Exploring the cosmological dynamics of a viable theory for ƒ(R)-gravity

Includes bibliographical references.A viable theory for ƒ(R) gravity, the Hu-Sawicki (HS) model, is considered from a dynamical systems perspective. The case for which n=1, c₁=1 is treated, and qualitative information regarding the phase space of this model is extracted. Several stable de Sitter equilibrium points are identified, as well as an unstable "matter-like" point and solution orbits which resemble the ACDM evolution are presented. The expansion history produced by integration of the dynamical system of the HS model is compared with that of ACDM. It is found that while the HS model can produce the desired behaviour in the appropriate regime, this occurs at the expense of ACDM values of the observational parameters

Investigating the parameter space of viable models for f(R) gravity

The accelerated expansion of spacetime intuitively points to the existence of new, unknown energy fields pervading the universe, but it is has also spurred the growth of the research field of modified gravity theories. Of these, f(R) theories of gravity is the first and simplest modification to General Relativity, and have been studied extensively for their astrophysical and cosmological predictions. Power law f(R) modifications have been shown to exhibit desirable characteristics, producing the late time accelerated expansion as well as satisfying local tests of gravity. However, there is wide degeneracy among models in this class, and they are known to suffer from cosmological instabilities, which could lead to curvature singularities at finite times. This thesis addresses questions directly relating to model degeneracy and sudden singularities. Cosmologies and cosmological perturbations, resulting from a general broken power law modification to GR are generated, studied and evolved. Simulations are performed using 1+3 space time decomposition of the field equations and a dynamical systems approach to f(R) cosmology. The parameter space of this model, which includes the HuSawicki [6], Starobinsky [96] and Miranda [7] f(R) forms as subclasses, is investigated. It is found that there are regions in the parameter space which are completely singular and bound by continuous curves. We also investigate regions of the parameter space in which the attractive nature of gravity is preserved, and find that these regions intersect. The results of a Markov Chain Monte Carlo analysis significantly narrowed the viable region of the exponent parameter space of the general power law f(R) model. Current cosmological distance data; SNIa (Union 2), BAO (6dFGS, BOSS, SDSS, WiggleZ) as well as the LRG power spectrum (SDSS DR9), were used to obtain these constraints. The best fits are compared with the ΛCDM model, and leads to the conclusion that this class is still a candidate for the gravitational interaction

On tidal forces in f(R) theories of gravity

Despite the extraordinary attention that modified gravity theories have attracted over the past decade, the geodesic deviation equation in this context has not received proper formulation thus far. This equation provides an elegant way to investigate the timelike, null and spacelike structure of spacetime geometries. In this investigation we provide the full derivation of this equation in situations where General Relativity has been extended in Robertson-Walker background spacetimes. We find that for null geodesics the contribution arising from the geometrical new terms is in general non-zero. Finally we apply the results to a well known class of f(R) theories, compare the results with General Relativity predictions and obtain the equivalent area distance relation.Comment: 9 pages, 2 figure

A Semi-Static Replication Method for Bermudan Swaptions under an Affine Multi-Factor Model

We present a semi-static replication algorithm for Bermudan swaptions under an affine, multi-factor term structure model. In contrast to dynamic replication, which needs to be continuously updated as the market moves, a semi-static replication needs to be rebalanced on just a finite number of instances. We show that the exotic derivative can be decomposed into a portfolio of vanilla discount bond options, which mirrors its value as the market moves and can be priced in closed form. This paves the way toward the efficient numerical simulation of xVA, market, and credit risk metrics for which forward valuation is the key ingredient. The static portfolio composition is obtained by regressing the target option’s value using an interpretable, artificial neural network. Leveraging the universal approximation power of neural networks, we prove that the replication error can be arbitrarily small for a sufficiently large portfolio. A direct, a lower bound, and an upper bound estimator for the Bermudan swaption price are inferred from the replication algorithm. Additionally, closed-form error margins to the price statistics are determined. We practically study the accuracy and convergence of the method through several numerical experiments. The results indicate that the semi-static replication approaches the LSM benchmark with basis point accuracy and provides tight, efficient error bounds. For in-model simulations, the semi-static replication outperforms a traditional dynamic hedge

An evaluation of professionalism of retail community pharmacists and quality of services provided to customers.

Thesis (MBA)-University of Natal, 2002.No abstract available

Uncovering the mesoscale structure of the credit default swap market to improve portfolio risk modelling

One of the most challenging aspects in the analysis and modelling of financial markets, including Credit Default Swap (CDS) markets, is the presence of an emergent, intermediate level of structure standing in between the microscopic dynamics of individual financial entities and the macroscopic dynamics of the market as a whole. This elusive, mesoscopic level of organisation is often sought for via factor models that ultimately decompose the market according to geographic regions and economic industries. However, at a more general level the presence of mesoscopic structure might be revealed in an entirely data-driven approach, looking for a modular and possibly hierarchical organisation of the empirical correlation matrix between financial time series. The crucial ingredient in such an approach is the definition of an appropriate null model for the correlation matrix. Recent research showed that community detection techniques developed for networks become intrinsically biased when applied to correlation matrices. For this reason, a method based on Random Matrix Theory has been developed, which identifies the optimal hierarchical decomposition of the system into internally correlated and mutually anti-correlated communities. Building upon this technique, here we resolve the mesoscopic structure of the CDS market and identify groups of issuers that cannot be traced back to standard industry/region taxonomies, thereby being inaccessible to standard factor models. We use this decomposition to introduce a novel default risk model that is shown to outperform more traditional alternatives.Comment: Quantitative Finance (2021