Nonparametric estimation for Levy processes with a view towards mathematical finance

Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model selection approach made up of two steps is investigated. The first step consists in the selection of a good estimator from a linear model of proposed Levy densities, while the second is a data-driven selection of a linear model among a given collection of linear models. By providing lower bounds for the minimax risk of estimation over Besov Levy densities, our estimators are shown to achieve the ``best'' rate of convergence. A numerical study for the case of histogram estimators and for variance Gamma processes, models of key importance in risky asset price modeling driven by Levy processes, is presented.Comment: 68 pages, 19 figures, submitted to Annals of Statistic

Parallel machine scheduling with precedence constraints and setup times

This paper presents different methods for solving parallel machine scheduling problems with precedence constraints and setup times between the jobs. Limited discrepancy search methods mixed with local search principles, dominance conditions and specific lower bounds are proposed. The proposed methods are evaluated on a set of randomly generated instances and compared with previous results from the literature and those obtained with an efficient commercial solver. We conclude that our propositions are quite competitive and our results even outperform other approaches in most cases

The energy scheduling problem: Industrial case-study and constraint propagation techniques

This paper deals with production scheduling involving energy constraints, typically electrical energy. We start by an industrial case-study for which we propose a two-step integer/constraint programming method. From the industrial problem we derive a generic problem,the Energy Scheduling Problem (EnSP). We propose an extension of specific resource constraint propagation techniques to efficiently prune the search space for EnSP solving. We also present a branching scheme to solve the problem via tree search.Finally,computational results are provided

Is implied correlation worth calculating? Evidence from foreign exchange options and historical data

Implied volatilities, as derived from option prices, have been shown to be useful in forecasting the subsequently observed volatility of the underlying financial variables. In this paper, we address the question of whether implied correlations, derived from options on the exchange rates in a currency trio, are useful in forecasting the observed correlations. We compare the forecast performance of the implied correlations from two currency trios with markedly different characteristics against correlation forecasts based on historical, time-series data. For the correlations in the USD/DEM/JPY currency trio, we find that implied correlations are useful in forecasting observed correlations, but they do not fully incorporate all the information in the historical data. For the correlations in the USD/DEM/CHF currency trio, implied correlations are much less useful. In general, since the performance of implied correlations varies across currency trios, implied correlations may not be worth calculating in all instances.Options (Finance) ; Foreign exchange

Evaluating covariance matrix forecasts in a value-at-risk framework

Covariance matrix forecasts of financial asset returns are an important component of current practice in financial risk management. A wide variety of models, ranging from matrices of simple summary measures to covariance matrices implied from option prices, are available for generating such forecasts. In this paper, we evaluate the relative accuracy of different covariance matrix forecasts using standard statistical loss functions and a value-at-risk (VaR) framework. This framework consists of hypothesis tests examining various properties of VaR models based on these forecasts as well as an evaluation using a regulatory loss function. ; Using a foreign exchange portfolio, we find that implied covariance matrix forecasts appear to perform best under standard statistical loss functions. However, within the economic context of a VaR framework, the performance of VaR models depends more on their distributional assumptions than on their covariance matrix specification. Of the forecasts examined, simple specifications, such as exponentially-weighted moving averages of past observations perform best with regard to the magnitude of VaR exceptions and regulatory capital requirements. These results provide empirical support for the commonly-used VaR models based on simple covariance matrix forecasts and distributional assumptions.Financial markets ; Risk ; Econometric models ; Forecasting

A simulated annealing algorithm for router nodes placement problem in Wireless Mesh Networks

Mesh router nodes placement is a central problem in Wireless Mesh Networks (WMNs). An efficient placement of mesh router nodes is indispensable for achieving network performance in terms of both network connectivity and user coverage. Unfortunately the problem is computationally hard to solve to optimality even for small deployment areas and a small number of mesh router nodes. As WMNs are becoming an important networking infrastructure for providing cost-efficient broadband wireless connectivity, researchers are paying attention to the resolution of the mesh router placement problem through heuristic approaches in order to achieve near optimal, yet high quality solutions in reasonable time. In this work we propose and evaluate a simulated annealing (SA) approach to placement of mesh router nodes in WMNs. The optimization model uses two maximization objectives, namely, the size of the giant component in the network and user coverage. Both objectives are important to deployment of WMNs; the former is crucial to achieve network connectivity while the later is an indicator of the QoS in WMNs. The SA approach distinguishes for its simplicity yet its policy of neighborhood exploration allows to reach promising areas of the solution space where quality solutions could be found. We have experimentally evaluated the SA algorithm through a benchmark of generated instances, varying from small to large size, and capturing different characteristics of WMNs such as topological placements of mesh clients. The experimental results showed the efficiency of the annealing approach for the placement of mesh router nodes in WMNs.Peer ReviewedPostprint (author's final draft

Unbalanced Workload Allocation in Large Assembly Lines.

In modern production systems that perform under high cost environments, even small improvements in line efficiency represents large savings over the lifetime of an assembly line. In the beginning of modern production systems, it was thought that a `perfectly balanced\u27 line was the most efficient way to design the line. However in practice, the ideal perfectly balanced line seldom occurs, because some degree of imbalance is inevitable. Recent studies have found that unbalanced lines with a bowl shape workload configuration can yield performance in throughput as good as, or even better than those of a perfectly balanced line. This thesis studied the bowl phenomenon in large unpaced assembly lines under stochastic processing times. The control variables analyzed in this study were line length, buffer capacity, task time variability, and percentage of imbalance. A full factorial experiment was designed in order to characterize the main and interaction effects, and computational simulation was used to replicate the behavior of the unbalanced assembly lines. The results of the experiment suggest that unbalancing a large assembly line in a bowl shape workload configuration could provide statistical significant improvements in throughput. Moreover, the results also suggest that the Work in Process (WIP) and the Cycle Time (CT) increase linearly as the Throughput (TR) of the line increases. Even though, the rate at which the TR increases is greater than the rate at which the WIP and CT increases, line designers and production managers need to make an important managerial decision on how much they are willing to increase the WIP and CT of their lines in order to improve the throughput when implementing a bowl shape workload configuration. Furthermore, the results suggested that as the buffer capacity and the number of workstations in the line decreases, and the coefficient of variation of the workstations increases the benefits the bowl phenomenon and the percentage of imbalance of the best bowl configuration increases. In this research, the relationship between the production rate of large assembly lines with a bowl shape workload configuration and its line length, buffer capacity, task time variability, and percentage of imbalance has been studied for the first time. The results would provide valuable guidelines for line designers and managers that want to improve their assembly lines

Motility of Swimming Bacteria Hydrodynamics and Statistics

The present work contains original research on the field of biophysics, specifically the study of swimming bacteria. Swimming microorganisms can be modeled as active particles moving at low Reynolds number (Re ≪ 1) and subject to different sources of noise. The term “active” means that they are self-propelled, while Re ≪ 1 implies that their motion is dominated by viscous stresses, therefore relying on non-reciprocal deformations in time, in order to achieve movement. Noise arises from thermal fluctuations and the inherent stochasticity of their propelling machinery, as a result, bacteria follow random trajectories. Nevertheless, bacteria have evolved to display a number of strategies to overcome randomness and achieve directed locomotion, known as “taxis”. Here, we explore the mechanisms involved in the propulsion and navigation of swimming bacteria, using low Reynolds number flow techniques and random walks. First, we introduce the physical principles that govern the dynamics of a low Reynolds number swimmer. We pay special attention to the random walk model for the description of the swimming trajectories, since it allows to quantify motility in terms of statistical measures, such as diffusivity and drift velocity, which can be measured experimentally. After a general discussion of the model, we demonstrate its use by applying it to the dynamics of bacteria-driven microswimmers, which are active particles that use bacteria as a propulsion mechanism. We show in particular, that the diffusivity of such particles increases with the square of their size and that the microswimmers inherit the chemotactic capabilities from the bacteria that propel them. These results are in agreement with experiments and can be useful to improve the design of these artificial microswimmers. Next, we investigate the motility properties of Spiroplasma melliferum, which is special among bacteria, as it can swim without flagella. Instead, Spiroplasma can switch the handedness of its helical body and in the process, the helical domains rotate generating propulsion. Based on experimental observations, we develop a hydrodynamic model to describe Spiroplasma motility. We obtain expressions for the total linear and angular displacements of the cell body per swimming stroke. Observing that the cell body does not reorient at the end of one period, we define an effective swimming speed and a hydrodynamic efficiency. Then, we show that the helical shape that maximises speed and efficiency has a pitch angle close to that of Spiroplasma, φ ≃ 35◦, in agreement with experimental observations and with previous numerical simulations. Finally, we explore the dynamics of a low Reynolds number swimmer crossing a viscosity gradient. This is a work in collaboration with experimental groups in the National University of Mexico (UNAM) and Brown University. The experiments aim to shed light on the dynamics of the bacterium Helicobacter pylori, which inhabits the human gut and is capable of penetrating the mucus layer that protects the stomach. Experimentally, a magnetic swimmer is immersed in a stratified solution of miscible fluids with different viscosities. The swimmer consists of a helical tail and a cylindrical head that rotate at a fixed rate due to the action of an external magnetic field. As the swimmer advances, it accelerates or slows down, depending on its orientation with respect to the gradient. In general, the experimental results show that it is harder for a pusher-like swimmer to swim up the gradient, whereas for a puller-like swimmer it is the opposite. We rationalize this mathematically by assuming that the forces acting on the swimmer depend on the local viscosity that it experiences. This allows us to calculate the swimming speed as a function of the swimmer’s position along the gradient. The predictions of the model are in good agreement with the experimental observations. The results also suggest that viscotaxis is possible without viscoreceptors, and in fact governed solely by the motility pattern of the swimmer. Together, the results presented in this thesis contribute to the understanding of bacterial motility and low Reynolds number swimmers in general. Furthermore, these results may be useful for future developments in biophysics, including applications to targeted drug delivery and microrobotics.European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement 682754 to Eric Lauga

UAV Formation Flight Utilizing a Low Cost, Open Source Configuration

The control of multiple unmanned aerial vehicles (UAVs) in a swarm or cooperative team scenario has been a topic of great interest for well over a decade, growing steadily with the advancements in UAV technologies. In the academic community, a majority of the studies conducted rely on simulation to test developed control strategies, with only a few institutions known to have nurtured the infrastructure required to propel multiple UAV control studies beyond simulation and into experimental testing. With the Cal Poly UAV FLOC Project, such an infrastructure was created, paving the way for future experimentation with multiple UAV control systems. The control system architecture presented was built on concepts developed in previous work by Cal Poly faculty and graduate students. An outer-loop formation flight controller based on a virtual waypoint implementation of potential function guidance was developed for use on an embedded microcontroller. A commercially-available autopilot system, designed for fully autonomous waypoint navigation utilizing low cost hardware and open source software, was modified to include the formation flight controller and an inter-UAV communication network. A hardware-in-the-loop (HIL) simulation was set up for multiple UAV testing and was utilized to verify the functionality of the modified autopilot system. HIL simulation results demonstrated leader-follower formation convergence to 15 meters as well as formation flight with three UAVs. Several sets of flight tests were conducted, demonstrating a successful leader-follower formation, but with relative distance convergence only reaching a steady state value of approximately 35 +/- 5 meters away from the leader

On the relationship between a graph and the cycle graph of its complement

From an arbitrary graph G, another graph called the cycle graph of G and denoted by C(G) can be derived. The cycle graph C(G) of G has as its vertices the chordless cycles of G and two vertices in C(G) are adjacent if and only if the corresponding chordless cycles have at least one edge in common