Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

The public management issues of access to electronic gaming machines (EGMs) : a case study of policy in Victoria, its effects and requirements for evaluation

Wynne and Schaffer (2003) have highlighted both the strong growth of gambling activity in recent years, and the revenue streams this has generated for governments and communities. Gambling activities and the revenues derived from them have, unsurprisingly, therefore also been seen as a way in which to increase economic development in deprived areas (Jinkner-Lloyd, 1996). Consequently, according to Brown et al (2003), gambling is now a large taxation revenue earner for many western governments, at both federal and state levels, worldwide (for example UK, USA, Australia). In size and importance, the Australian gambling industry in particular has grown significantly over the last three decades, experiencing a fourfold increase in real gambling turnover. There are, however, also concerns expressed about gambling and Electronic Gaming in particular, as illustrated in economic, social and ethical terms in Oddo (1997). There are also spatial aspects to understanding these issues. Marshall’s (1998) study, for example, highlights that benefits from gambling are more likely to accrue at the macro as opposed to the local level, because of centralised tax gathering and spending of tax revenues, whilst localities may suffer from displacement of activities with higher multipliers than the institutions with EGMs that replace them. This also highlights a regional context of costs, where benefits accrue to the centre, but the costs accrue to the regions and localities, as simultaneously resources leave those communities through both the gambling activities themselves (in the form of revenue for the EGM owners), and the government (through taxes).

Report : stochastic analysis of road asset data for maintenance cost prediction

Reliable budget/cost estimates for road maintenance and rehabilitation are subjected to uncertainties and variability in road asset condition and characteristics of road users. The CRC CI research project 2003-029-C ‘Maintenance Cost Prediction for Road’ developed a method for assessing variation and reliability in budget/cost estimates for road maintenance and rehabilitation. The method is based on probability-based reliable theory and statistical method. The next stage of the current project is to apply the developed method to predict maintenance/rehabilitation budgets/costs of large networks for strategic investment. The first task is to assess the variability of road data. This report presents initial results of the analysis in assessing the variability of road data. A case study of the analysis for dry non reactive soil is presented to demonstrate the concept in analysing the variability of road data for large road networks. In assessing the variability of road data, large road networks were categorised into categories with common characteristics according to soil and climatic conditions, pavement conditions, pavement types, surface types and annual average daily traffic. The probability distributions, statistical means, and standard deviation values of asset conditions and annual average daily traffic for each type were quantified. The probability distributions and the statistical information obtained in this analysis will be used to asset the variation and reliability in budget/cost estimates in later stage. Generally, we usually used mean values of asset data of each category as input values for investment analysis. The variability of asset data in each category is not taken into account. This analysis method demonstrated that it can be used for practical application taking into account the variability of road data in analysing large road networks for maintenance/rehabilitation investment analysis.

Synthesis of orchestrators from service choreographies

With service interaction modelling, it is customary to distinguish between two types of models: choreographies and orchestrations. A choreography describes interactions within a collection of services from a global perspective, where no service plays a privileged role. Instead, services interact in a peer-to-peer manner. In contrast, an orchestration describes the interactions between one particular service, the orchestrator, and a number of partner services. The main proposition of this work is an approach to bridge these two modelling viewpoints by synthesising orchestrators from choreographies. To start with, choreographies are defined using a simple behaviour description language based on communicating finite state machines. From such a model, orchestrators are initially synthesised in the form of state machines. It turns out that state machines are not suitable for orchestration modelling, because orchestrators generally need to engage in concurrent interactions. To address this issue, a technique is proposed to transform state machines into process models in the Business Process Modelling Notation (BPMN). Orchestrations represented in BPMN can then be augmented with additional business logic to achieve value-adding mediation. In addition, techniques exist for refining BPMN models into executable process definitions. The transformation from state machines to BPMN relies on Petri nets as an intermediary representation and leverages techniques from theory of regions to identify concurrency in the initial Petri net. Once concurrency has been identified, the resulting Petri net is transformed into a BPMN model. The original contributions of this work are: an algorithm to synthesise orchestrators from choreographies and a rules-based transformation from Petri nets into BPMN.

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

Temporal-based support vector machines for facial expression recognition

When classifying a signal, ideally we want our classifier to trigger a large response when it encounters a positive example and have little to no response for all other examples. Unfortunately in practice this does not occur with responses fluctuating, often causing false alarms. There exists a myriad of reasons why this is the case, most notably not incorporating the dynamics of the signal into the classification. In facial expression recognition, this has been highlighted as one major research question. In this paper we present a novel technique which incorporates the dynamics of the signal which can produce a strong response when the peak expression is found and essentially suppresses all other responses as much as possible. We conducted preliminary experiments on the extended Cohn-Kanade (CK+) database which shows its benefits. The ability to automatically and accurately recognize facial expressions of drivers is highly relevant to the automobile. For example, the early recognition of “surprise” could indicate that an accident is about to occur; and various safeguards could immediately be deployed to avoid or minimize injury and damage. In this paper, we conducted initial experiments on the extended Cohn-Kanade (CK+) database which shows its benefits.