libstable: Fast, Parallel, and High-Precision Computation of α-Stable Distributions in R, C/C++, and MATLAB

α-stable distributions are a family of well-known probability distributions. However, the lack of closed analytical expressions hinders their application. Currently, several tools have been developed to numerically evaluate their density and distribution functions or to estimate their parameters, but available solutions either do not reach sufficient precision on their evaluations or are excessively slow for practical purposes. Moreover, they do not take full advantage of the parallel processing capabilities of current multi-core machines. Other solutions work only on a subset of the α-stable parameter space. In this paper we present an R package and a C/C++ library with a MATLAB front-end that permit parallelized, fast and high precision evaluation of density, distribution and quantile functions, as well as random variable generation and parameter estimation of α-stable distributions in their whole parameter space. The described library can be easily integrated into third party developments

Correlated disorder in myelinated axons orientational geometry and structure

While the ultrastructure of the myelin has been considered to be a quasi-crystalline stable system, nowadays its multiscale complex dynamics appears to play a key role for its functionality, degeneration and repair processes following neurological diseases and trauma. In this work, we have investigated the axons interactions associated to the nerve functionality, measuring the spatial distribution of the orientational fluctuations of axons in a Xenopus Laevis sciatic nerve. At this aim, we have used Scanning micro X-ray Diffraction (SmXRD), a non-invasive already applied to other heterogeneous systems presenting complex geometries from microscale to nanoscale. We have found that the orientational spatial fluctuations of fresh axons show a correlated disorder described by Levy flight distribution. Thus, we have studied how this correlated disorder evolves during the degeneration of the nerve. Our results show that the spatial distribution of axons orientational fluctuations in unfresh, aged nerve loose the correlated disorder assuming a randomly disordered behaviour. This work allows a deeper understanding of nerve states and paves the way to study other materials and biomaterials with the same technique to detect and to characterize their states and supramolecular structure, associated with dynamic structural changes at the nanoscale and mesoscale.Comment: 9 pages, 4 figure

Models for Heavy-tailed Asset Returns

Many of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the Black- Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR – rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model – the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the socalled truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples.Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Asset return; Random number generation; Parameter estimation

Evolution of Complexity in Out-of-Equilibrium Systems by Time-Resolved or Space-Resolved Synchrotron Radiation Techniques

Out-of-equilibrium phenomena are attracting high interest in physics, materials science, chemistry and life sciences. In this state, the study of structural fluctuations at different length scales in time and space are necessary to achieve significant advances in the understanding of structure-functionality relationship. The visualization of patterns arising from spatiotemporal fluctuations is nowadays possible thanks to new advances in X-ray instrumentation development that combine high resolution both in space and in time. We present novel experimental approaches using high brilliance synchrotron radiation sources, fast detectors and focusing optics, joint with advanced data analysis based on automated statistical, mathematical and imaging processing tools. This approach has been used to investigate structural fluctuations in out-of-equilibrium systems in the novel field of inhomogeneous quantum complex matter at the crossing point of technology, physics and biology. In particular, we discuss how nanoscale complexity controls the emergence of high temperature superconductivity (HTS), myelin functionality and formation of hybrid organic-inorganic nanostructures. The emergent complex geometries, opening novel venues to quantum technology and to development of quantum physics of living systems, are discussedComment: 18 pages, 7 figure

A Review of the Fractal Market Hypothesis for Trading and Market Price Prediction

This paper provides a review of the Fractal Market Hypothesis (FMH) focusing on financial times series analysis. In order to put the FMH into a broader perspective, the Random Walk and Efficient Market Hypotheses are considered together with the basic principles of fractal geometry. After exploring the historical developments associated with different financial hypotheses, an overview of the basic mathematical modelling is provided. The principal goal of this paper is to consider the intrinsic scaling properties that are characteristic for each hypothesis. In regard to the FMH, it is explained why a financial time series can be taken to be characterised by a 1/t1−1/γ role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3e1/t1−1/γ scaling law, where γ\u3e0 role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eγ\u3e0 is the Lévy index, which is able to quantify the likelihood of extreme changes in price differences occurring (or otherwise). In this context, the paper explores how the Lévy index, coupled with other metrics, such as the Lyapunov Exponent and the Volatility, can be combined to provide long-term forecasts. Using these forecasts as a quantification for risk assessment, short-term price predictions are considered using a machine learning approach to evolve a nonlinear formula that simulates price values. A short case study is presented which reports on the use of this approach to forecast Bitcoin exchange rate values

A review of the fractal market hypothesis for trading and market price prediction

This paper provides a review of the Fractal Market Hypothesis (FMH) focusing on financial times series analysis. In order to put the FMH into a broader perspective, the Random Walk and Efficient Market Hypotheses are considered together with the basic principles of fractal geometry. After exploring the historical developments associated with different financial hypotheses, an overview of the basic mathematical modelling is provided. The principal goal of this paper is to consider the intrinsic scaling properties that are characteristic for each hypothesis. In regard to the FMH, it is explained why a financial time series can be taken to be characterised by a 1/t 1−1/γ scaling law, where γ > 0 is the Lévy index, which is able to quantify the likelihood of extreme changes in price differences occurring (or otherwise). In this context, the paper explores how the Lévy index, coupled with other metrics, such as the Lyapunov Exponent and the Volatility, can be combined to provide long-term forecasts. Using these forecasts as a quantification for risk assessment, short-term price predictions are considered using a machine learning approach to evolve a nonlinear formula that simulates price values. A short case study is presented which reports on the use of this approach to forecast Bitcoin exchange rate values

Stochastic volatility models in financial econometrics: an application to South Africa

Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Commerce, Law & Management, School of Economic and Business Sciences, 2015.The dissertation carries out a study to understand asset price behaviour in South Africa. This is investigated through the application of stochastic volatility models to trace the characteristics of high frequency financial data; daily temperature, exchange rates, interest rates, stock and house prices. Innovation in the derivatives market has seen the introduction of weather derivatives as a risk mitigation tool against adverse weather movements. Chapter Two applies three different time series models of temperature to estimate payoffs to determine which method offers the best hedging strategy in four South African cities. Results from the study suggest that the seasonality GARCH method of estimating payoffs for temperature based weather derivatives offers superior performance compared to the Cumulative Cooling Degree Days (CDD) and the historical method. This suggests that the seasonality GARCH method can be applied in these cities to hedge against adverse temperature movements. In Chapter three we consider the estimation methodology for jump diffusion models and GARCH models. Chapter four investigates volatility on exchange rate data. Use is made of the british pound/south african rand, euro/south african rand and u.s dollar/ south african rand exchange rates. The research introduces a jump diffusion model to trace the behaviour of exchange rate data. Estimation results are able to match the summary statistics in mean, variance, skewness and kurtosis. Results from the model can also explain the volatility smile for short and medium term maturities. A fat tailed GARCH model is introduced to capture the persistence in volatility on exchange rate data. Results from this chapter have an implication for pricing currency options to offer leverage to organisations affected by exchange rate risk. Chapter five extends the analysis to study the behaviour of short term interest rates, making use of the 90 Day Treasury bill (T-Bill) rate. The chapter considers a variant application of the Chan et al. (1992) model for short term interest rates wherein a jump diffusion model is introduced. The results match the summary statistics equivalent suggesting the capability of the model specification. Splitting the estimation period suggests that the jump size is highest post inflation target though with a smaller intensity. However, the 90 Day T-Bill shows higher volatility after inflation targeting though with a lesser intensity. These findings have a bearing on valuation of short term interest derivatives and also investigating multi factor models of interest rates. In chapter six four vi sectors (banking, mining, media and leisure) are considered to explore movements in stock prices. A jump diffusion model is applied to get estimation results. The results confirm related studies that stock prices have incidents of volatility which can be captured by a jump diffusion model. The results also shed light on the importance of portfolio diversification considering the different results across the sectors investigated. The implication also lies in understanding market efficiency. Chapter seven applies the jump diffusion model on house prices to understand more on the drivers of volatility on house prices. The interesting results on this chapter can be summarised as follows; the four different house segments have almost similar jump sizes though the small house price segment has highest intensity. This can point to expectations and volatility from participants in this segment at a higher level than for other segments over different regimes over the study period. The estimated higher moments were not normalised as had happened for the three previous chapters after introducing the jump diffusion model. Results from this chapter have an application to valuing mortgage premium across different house price segments. It is recommended that rigorous research on asset prices using various approaches be considered as it goes a long way in informing policy makers and investors to mitigate risk in an environment of volatile asset prices. With the growing interest in weather derivatives world-wide, there is a need to educate farmers, government entities, potential counter-parties and other organisations affected by weather related risk on the importance of weather derivatives so that a foundation is laid for trading in this special type of insurance

Adaptive and learning-based formation control of swarm robots

Autonomous aerial and wheeled mobile robots play a major role in tasks such as search and rescue, transportation, monitoring, and inspection. However, these operations are faced with a few open challenges including robust autonomy, and adaptive coordination based on the environment and operating conditions, particularly in swarm robots with limited communication and perception capabilities. Furthermore, the computational complexity increases exponentially with the number of robots in the swarm. This thesis examines two different aspects of the formation control problem. On the one hand, we investigate how formation could be performed by swarm robots with limited communication and perception (e.g., Crazyflie nano quadrotor). On the other hand, we explore human-swarm interaction (HSI) and different shared-control mechanisms between human and swarm robots (e.g., BristleBot) for artistic creation. In particular, we combine bio-inspired (i.e., flocking, foraging) techniques with learning-based control strategies (using artificial neural networks) for adaptive control of multi- robots. We first review how learning-based control and networked dynamical systems can be used to assign distributed and decentralized policies to individual robots such that the desired formation emerges from their collective behavior. We proceed by presenting a novel flocking control for UAV swarm using deep reinforcement learning. We formulate the flocking formation problem as a partially observable Markov decision process (POMDP), and consider a leader-follower configuration, where consensus among all UAVs is used to train a shared control policy, and each UAV performs actions based on the local information it collects. In addition, to avoid collision among UAVs and guarantee flocking and navigation, a reward function is added with the global flocking maintenance, mutual reward, and a collision penalty. We adapt deep deterministic policy gradient (DDPG) with centralized training and decentralized execution to obtain the flocking control policy using actor-critic networks and a global state space matrix. In the context of swarm robotics in arts, we investigate how the formation paradigm can serve as an interaction modality for artists to aesthetically utilize swarms. In particular, we explore particle swarm optimization (PSO) and random walk to control the communication between a team of robots with swarming behavior for musical creation