https://www.um.edu.mt/library/oar/handle/123456789/77882 2026-04-16T05:04:17Z https://www.um.edu.mt/library/oar/handle/123456789/93898 Title: Controlling stochastic currency risk exposure optimally Abstract: Investors operating in countries adopting different currencies face an additional risk in the form of currency exchange rates. This thesis aims at deriving the optimal hedging strategy for such investors through the use of futures and forwards. Having described the processes underlying the economic framework which affect the investor, the theory of stochastic optimal control will be used to formulate and solve this the problem mathematically. As an attempt to solve the problem analytically, the dynamic programming approach will first be employed. However, since the resulting Hamilton-Jacobi-Bellman equation involves a highly non-linear second order partial differential equation, such a solution is hard to obtain in closed form and so we resort to numerical techniques. To this end we shall employ the Markov chain approximation method, in which a sequence of optimal stochastic control problems for Markov chains will be solved via the dynamic programming approach. The latter will lead to a sequence of functional equations, which have to be solved for the approximating value function. An approximate solution to these functional equations will then be obtained numerically via the Implicit method which, provided the approximating Markov chains are locally consistent, converges to the original controlled stochastic integral equation. Furthermore under this local consistency, the solutions to the functional equations are also known to converge to the value function of the original stochastic optimal control problem. Description: B.SC.(HONS)STATS.&OP.RESEARCH 2016-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/93803 Title: Interior point methods for linear programming Abstract: The introduction of interior point methods came about as an alternative linear programming solver to Dantzig's Simplex algorithm. In this dissertation, we will study a series of methods with a polynomial-time order which offer superior theoretical properties and improved efficiency features when compared to an exponential-time order method such as the Simplex algorithm. This class of methods from the optimization field solves linear programs by searching for an optimal point through the interior of the feasible region, as opposed to the Simplex' s approach of searching along the boundaries. We will study interior point methods such as the Ellipsoid algorithm, Karmarkar's Projective algorithm and the Primal-Dual Path-Following algorithm. This dissertation addresses the complexity issues of such algorithms, puts them into practice using software such as MATLAB and Mathematica, compares their performance with the Simplex's performance and aims to conclude which algorithm (or type of algorithm) is the most efficient solver for linear programs. Description: B.SC.(HONS)STATS.&OP.RESEARCH 2016-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/93791 Title: Analysing the properties of ordinary least squares estimators of regression models in the presence of time series variables Abstract: Regression analysis is amongst one of the most popular statistical techniques which has been studied extensively in the past decades. A different approach to the classical linear regression arises when the dependent variable and its predictors are regarded as time series variables, therefore the observations in the study are no longer independent. This dissertation studies the properties of the ordinary least squares estimators when time series variables are considered and when the assumptions of classical linear regression are violated. The distribution of the estimator when these assumptions are not satisfied is derived and the relevant time series regression models are applied to various datasets to model the accounting revenue and turnover of a local betting company Description: B.SC.(HONS)STATS.&OP.RESEARCH 2016-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/93789 Title: Gaussian process classification of sportsbook customers Abstract: Segmentation is an underrated tool in management science that in many times implemented for different purposes, marketing being the more common. Classification o customers could be of great use to the online betting industry. In this dissertation, we shall use segmentation techniques on a sportsbook dataset using a number of customer characteristics as well as playing habits and performances. Gaussian processes have been much studied and harnessed to aid with diverse problems in statistics; regression and classification being major beneficiaries. In the work developed here techniques using Gaussian processes are considered at length studied and applied to the data. Classical clustering techniques offered benchmarks, background and context for comparative and evaluative purposes. Description: B.SC.(HONS)STATS.&OP.RESEARCH 2016-01-01T00:00:00Z