BURA Collection:http://bura.brunel.ac.uk/handle/2438/2352016-05-25T13:14:17Z2016-05-25T13:14:17ZDevelopment and evaluation of computer-aided assessment in discrete and decision mathematicsZaczek, Kingahttp://bura.brunel.ac.uk/handle/2438/109732015-06-09T02:00:29Z2015-01-01T00:00:00ZTitle: Development and evaluation of computer-aided assessment in discrete and decision mathematics
Authors: Zaczek, Kinga
Abstract: This thesis describes the development of Computer-Aided Assessment questions for elementary discrete and decision mathematics at the school/university interface, stressing the pedagogy behind the questions’ design and the development of methodology for assessing their efficacy in improving students’ engagement and perceptions, as well as on their exams results. The questions give instant and detailed feedback and hence are valuable as diagnostic, formative or summative tools. A total of 275 questions were designed and coded for five topics, numbers, sets, logic, linear programming and graph theory, commonly taught to students of mathematics, computer science, engineering and management. Pedagogy and programming problems with authoring questions were resolved and are discussed in specific topic contexts and beyond. The delivery of robust and valid objective questions, even within the constraints of CAA, is therefore feasible. Different question types and rich feedback comprising text, equations and diagrams that allow random parameters to produce millions of realisations at run time, can give CAA an important role in teaching mathematics at this level. Questionnaires identified that CAA was generally popular with students, with the vast majority seeing CAA not only as assessment but also as a learning resource. To test the impact of CAA on students’ learning, an analysis of the exam scripts quantified its effect on class means and standard deviations. This also identified common student errors, which fed into the question design and editing processes by providing evidence-based mal-rules. Four easily-identified indicators (correctly-written remainders, conversion of binary/octal/hexadecimal numbers, use of correct set notation {…} and consistent layout of truth tables) were examined in student exam scripts to find out if the CAA helps students to improve examination answers. The CAA answer files also provided the questions’ facilities and discriminations, potentially giving teachers specific information on which to base and develop their teaching and assessment strategies. We conclude that CAA is a successful tool for the formative/summative assessment of mathematics at this level and has a positive effect on students’ learning.
Description: This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University London.2015-01-01T00:00:00ZSolving cardinality constrained portfolio optimisation problem using genetic algorithms and ant colony optimisationLi, Yibohttp://bura.brunel.ac.uk/handle/2438/108672015-05-19T08:25:43Z2015-01-01T00:00:00ZTitle: Solving cardinality constrained portfolio optimisation problem using genetic algorithms and ant colony optimisation
Authors: Li, Yibo
Abstract: In this thesis we consider solution approaches for the index tacking problem, in which we aim to reproduces the performance of a market index without purchasing all of the stocks that constitute the index. We solve the problem using three different solution approaches: Mixed Integer Programming (MIP), Genetic Algorithms (GAs), and Ant-colony Optimization (ACO) Algorithm by limiting the number of stocks that can be held. Each index is also assigned with different cardinalities to examine the change to the solution values. All of the solution approaches are tested by considering eight market indices. The smallest data set only consists of 31 stocks whereas the largest data set includes over 2000 stocks. The computational results from the MIP are used as the benchmark to measure the performance of the other solution approaches. The Computational results are presented for different solution approaches and conclusions are given. Finally, we implement post analysis and investigate the best tracking portfolios achieved from the three solution approaches. We summarise the findings of the investigation, and in turn, we further improve some of the algorithms. As the formulations of these problems are mixed-integer linear programs, we use the solver ‘Cplex’ to solve the problems. All of the programming is coded in AMPL.
Description: This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London2015-01-01T00:00:00ZComplex networks with node intrinsic fitness: on structural properties and contagious phenomenaHoppe, Konradhttp://bura.brunel.ac.uk/handle/2438/103452015-03-06T03:00:22Z2014-01-01T00:00:00ZTitle: Complex networks with node intrinsic fitness: on structural properties and contagious phenomena
Authors: Hoppe, Konrad
Abstract: Complex networks is a vibrant research field and has received much attention over the last decade. Central to this area is the question of how networks around us are constructed. The essential notion of network research is that these systems are assembled in a decentralised way, thus no central agent is planning the network beforehand. Despite this lack of central coordination, many networks present intriguing universalities, such as broad degree distributions, in the form of power-laws. The subject of study in this thesis is a class of networks that are constructed by a node intrinsic variable, called fitness. The way these networks grow could be called a rich-get-richer mechanism. The fitter a node is, the more likely it is to acquire new connections inside the network. Several aspects that are directly connected to these networks are explored in this thesis. In the first part, the properties of growing networks that are driven by fitness are investigated and it is shown that the introduction of growth leads to a topological structure that is different from its static counterpart. In the subsequent chapter, percolation on fitness driven networks is studied. The results give insights into possible mechanisms that can stabilise systems. Furthermore, the theory can be used to identify vulnerable structures around us. In the following chapter, the world trade network is discussed. This numerical investigation highlights possible improvements to the methodology to make statistical analysis more robust. That chapter is followed by an analysis of time-varying networks.Time-varying networks represent an interesting construct that allows a formulation of stochastic processes on the same time-scale as the evolution of the network itself. This possibility is highly relevant to the investigation of epidemics, for instance. In the last chapter, a study of a system of clusters and their self-organised formation is presented.
Description: This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University London.2014-01-01T00:00:00ZStochastic models with random parameters for financial marketsIslyaev, Surenhttp://bura.brunel.ac.uk/handle/2438/103442015-03-06T03:00:28Z2014-01-01T00:00:00ZTitle: Stochastic models with random parameters for financial markets
Authors: Islyaev, Suren
Abstract: The aim of this thesis is a development of a new class of financial models with
random parameters, which are computationally efficient and have the same
level of performance as existing ones. In particular, this research is threefold.
I have studied the evolution of storable commodity and commodity futures
prices in time using a new random parameter model coupled with a Kalman
filter. Such a combination allows one to forecast arbitrage-free futures prices
and commodity spot prices one step ahead.
Another direction of my research is a new volatility model, where the
volatility is a random variable. The main advantage of this model is high
calibration speed compared to the existing stochastic volatility models such as
the Bates model or the Heston model. However, the performance of the new
model is comparable to the latter. Comprehensive numerical studies demonstrate
that the new model is a very competitive alternative to the Heston or
the Bates model in terms of accuracy of matching option prices or computing
hedging parameters.
Finally, a new futures pricing model for electricity futures prices was developed.
The new model has a random volatility parameter in its underlying
process. The new model has less parameters, as compared to two-factor models
for electricity commodity pricing with and without jumps. Numerical experiments
with real data illustrate that it is quite competitive with the existing
two-factor models in terms of pricing one step ahead futures prices, while being
far simpler to calibrate. Further, a new heuristic for calibrating two-factor
models was proposed. The new calibration procedure has two stages, offline
and online. The offline stage calibrates parameters under a physical measure,
while the online stage is used to calibrate the risk-neutrality parameters on
each iteration of the particle filter. A particle filter was used to estimate the
values of the underlying stochastic processes and to forecast futures prices one
step ahead.
The contributory material from two chapters of this thesis have been submitted
to peer reviewed journals in terms of two papers:
• Chapter 4: “A fast calibrating volatility model” has been submitted to
the European Journal of Operational Research.
• Chapter 5: “Electricity futures price models : calibration and forecasting”
has been submitted to the European Journal of Operational Research.
Description: This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University London.2014-01-01T00:00:00Z