Numerical solutions of stochastic differential equations – implementation and stability issues

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

Mobius markets : professional families in rural educational markets

Australia has many isolated communities that require human services provided by qualified professionals. Maintaining a viable and equitable spread of such educational capital across space as a public good is a challenge. Reports investigating this problem repeatedly point to ‘family issues’ such as limited options for children’s education, and limited access to ongoing professional development, as deterrents for rural/remote employment despite lucrative incentive schemes. This paper draws on semi-structured interviews with 30 parents of school-aged children, who work as doctors, nurses, teachers and police in six rural/remote towns in Queensland. We asked them how their family units reconcile career opportunities with educational strategy for family members over time and space. This paper considers these issues as a sociology of education problem in a context of educational marketisation and spiralling credentialism. This paper offers the concept of ‘mobius markets’ to capture the cyclical and intergenerational process underway in middle class professional families of investing in educational capitals, maintaining or maximising their value and profiting from them. A mobius strip is the topological anomaly of a single loop with one twist in it, whereby the loop becomes one continuous surface, not the double-sided shape it appears to be. This project is interested in how the middle class professional family is similarly on a constant circuit, investing in educational capitals, upgrading their currency/value, and profiting from them. This elaborated sense of educational markets extends the more usual sociological focus on school choice.

Destination brand equity for Australia : testing a model of CBBE in short haul and long haul markets

The study of destination brand performance measurement has only emerged in earnest as a field in the tourism literature since 2007. The concept of consumer-based brand equity (CBBE) is gaining favour from services marketing researchers as an alternative to the traditional ‘net-present-value of future earnings’ method of measuring brand equity. The perceptions-based CBBE model also appears suitable for examining destination brand performance, where a financial brand equity valuation on a destination marketing organisation’s (DMO) balance sheet is largely irrelevant. This is the first study to test and compare the model in both short and long haul markets. The paper reports the results of tests of a CBBE model for Australia in a traditional short haul market (New Zealand) and an emerging long haul market (Chile). The data from both samples indicated destination brand salience, brand image, and brand value are positively related to purchase intent for Australia in these two disparate markets.

Improved estimates of percolation and anisotropic permeability from 3-D X-ray microtomography using stochastic analyses and visualization

X-ray microtomography (micro-CT) with micron resolution enables new ways of characterizing microstructures and opens pathways for forward calculations of multiscale rock properties. A quantitative characterization of the microstructure is the first step in this challenge. We developed a new approach to extract scale-dependent characteristics of porosity, percolation, and anisotropic permeability from 3-D microstructural models of rocks. The Hoshen-Kopelman algorithm of percolation theory is employed for a standard percolation analysis. The anisotropy of permeability is calculated by means of the star volume distribution approach. The local porosity distribution and local percolation probability are obtained by using the local porosity theory. Additionally, the local anisotropy distribution is defined and analyzed through two empirical probability density functions, the isotropy index and the elongation index. For such a high-resolution data set, the typical data sizes of the CT images are on the order of gigabytes to tens of gigabytes; thus an extremely large number of calculations are required. To resolve this large memory problem parallelization in OpenMP was used to optimally harness the shared memory infrastructure on cache coherent Non-Uniform Memory Access architecture machines such as the iVEC SGI Altix 3700Bx2 Supercomputer. We see adequate visualization of the results as an important element in this first pioneering study.

Essays on volatility and liquidity in financial markets

The price formation of financial assets is a complex process. It extends beyond the standard economic paradigm of supply and demand to the understanding of the dynamic behavior of price variability, the price impact of information, and the implications of trading behavior of market participants on prices. In this thesis, I study aggregate market and individual assets volatility, liquidity dimensions, and causes of mispricing for US equities over a recent sample period. How volatility forecasts are modeled, what determines intradaily jumps and causes changes in intradaily volatility and what drives the premium of traded equity indexes? Are they induced, for example, by the information content of lagged volatility and return parameters or by macroeconomic news, changes in liquidity and volatility? Besides satisfying our intellectual curiosity, answers to these questions are of direct importance to investors developing trading strategies, policy makers evaluating macroeconomic policies and to arbitrageurs exploiting mispricing in exchange-traded funds. Results show that the leverage effect and lagged absolute returns improve forecasts of continuous components of daily realized volatility as well as jumps. Implied volatility does not subsume the information content of lagged returns in forecasting realized volatility and its components. The reported results are linked to the heterogeneous market hypothesis and demonstrate the validity of extending the hypothesis to returns. Depth shocks, signed order flow, the number of trades, and resiliency are the most important determinants of intradaily volatility. In contrast, spread shock and resiliency are predictive of signed intradaily jumps. There are fewer macroeconomic news announcement surprises that cause extreme price movements or jumps than those that elevate intradaily volatility. Finally, the premium of exchange-traded funds is significantly associated with momentum in net asset value and a number of liquidity parameters including the spread, traded volume, and illiquidity. The mispricing of industry exchange traded funds suggest that limits to arbitrage are driven by potential illiquidity.

China’s new creative strategy : the utilization of cultural soft power and new markets

This book examines different aspects of Asian popular culture, including films, TV, music, comedy, folklore, cultural icons, the Internet and theme parks. It raises important questions such as – What are the implications of popularity of Asian popular culture for globalization? Do regional forces impede the globalizing of cultures? Or does the Asian popular culture flow act as a catalyst or conveying channel for cultural globalization? Does the globalization of culture pose a threat to local culture? It addresses two seemingly contradictory and yet parallel processes in the circulation of Asian popular culture: the interconnectedness between Asian popular culture and western culture in an era of cultural globalization that turns subjects such as Pokémon, Hip Hop or Cosmopolitan into truly global phenomena, and the local derivatives and versions of global culture that are necessarily disconnected from their origins in order to cater for the local market. It thereby presents a collective argument that, whilst local social formations, and patterns of consumption and participation in Asia are still very much dependent on global cultural developments and the phenomena of modernity, yet such dependence is often concretized, reshaped and distorted by the local media to cater for the local market. Contents: Introduction: Asian Popular Culture: The Global (Dis)continuity Anthony Y.H. Fung Part 1: The Dominance of Global Continuity: Cultural Localization and Adaptation 1. One Region, Two Modernities: Disneyland in Tokyo and Hong Kong Micky Lee and Anthony Y.H. Fung 2. Comic Travels: Disney Publishing in the People’s Republic of China Jennifer Altehenger 3. When Chinese Youth Meet Harry Potter: Translating Consumption and Middle Class Identification John Nguyet Erni 4.New Forms of Transborder Visuality in Urban China: Saving Face for Magazine Covers Eric Kit-Wai Ma 5. Cultural Consumption and Masculinity: A Case Study of GQ Magazine Covers in Taiwan Hong-Chi Shiau Part 2: Global Discontinuity: The Local Absorption of Global Culture 6. An Unlocalized and Unglobalized Subculture: English Language Independent Music in Singapore Kai Khiun Liew and Shzr Ee Tan 7. The Localized Production of Jamaican Music in Thailand Viriya Sawangchot 8. Consuming Online Games in Taiwan: Global Games and Local Market Lai-Chi Chen 9. The Rise of the Korean Cinema in Inbound and Outbound Globalization Shin Dong Kim Part 3: Cultural Domestication: A New Form of Global Continuity 10. Pocket Capitalism and Virtual Intimacy: Pokémon as a Symptom of Post-Industrial Youth Culture Anne Allison 11. Playing the Global Game: Japan Brand and Globalization Kukhee Choo Part 4: China as a Rising Market: Cultural Antagonism and Globalization 12. China’s New Creative Strategy: The Utilization of Cultural Soft Power and New Markets Michael Keane and Bonnie Liu 13. Renationalizing Hong Kong Cinema: The Gathering Force of the Mainland Market Michael Curtin

How distributional preferences shape incentives on (experimental) markets for credence goods

Credence goods markets suffer from inefficiencies caused by superior information of sellers about the surplus-maximizing quality. While standard theory predicts that equal mark-up prices solve the credence goods problem if customers can verify the quality received, experimental evidence indicates the opposite. We identify a lack of robustness of institutional design with respect to heterogeneity in distributional preferences as a possible cause and design new experiments that allow for parsimonious identification of sellers’ distributional types. Our results indicate that less than a fourth of the subjects behave according to standard theory’s assumption, the rest behaving either in line with non-standard selfish or in accordance with non-trivial other-regarding preferences. We discuss consequences of our findings for institutional design and agent selection.

Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes

Mathematical descriptions of birth–death–movement processes are often calibrated to measurements from cell biology experiments to quantify tissue growth rates. Here we describe and analyze a discrete model of a birth–death-movement process applied to a typical two–dimensional cell biology experiment. We present three different descriptions of the system: (i) a standard mean–field description which neglects correlation effects and clustering; (ii) a moment dynamics description which approximately incorporates correlation and clustering effects, and; (iii) averaged data from repeated discrete simulations which directly incorporates correlation and clustering effects. Comparing these three descriptions indicates that the mean–field and moment dynamics approaches are valid only for certain parameter regimes, and that both these descriptions fail to make accurate predictions of the system for sufficiently fast birth and death rates where the effects of spatial correlations and clustering are sufficiently strong. Without any method to distinguish between the parameter regimes where these three descriptions are valid, it is possible that either the mean–field or moment dynamics model could be calibrated to experimental data under inappropriate conditions, leading to errors in parameter estimation. In this work we demonstrate that a simple measurement of agent clustering and correlation, based on coordination number data, provides an indirect measure of agent correlation and clustering effects, and can therefore be used to make a distinction between the validity of the different descriptions of the birth–death–movement process.

Heat-producing crust regulation of subsurface temperatures : a stochastic model re-evaluation of the geothermal potential in western Queensland, Australia

A large subsurface, elevated temperature anomaly is well documented in Central Australia. High Heat Producing Granites (HHPGs) intersected by drilling at Innamincka are often assumed to be the dominant cause of the elevated subsurface temperatures, although their presence in other parts of the temperature anomaly has not been confirmed. Geological controls on the temperature anomaly remain poorly understood. Additionally, methods previously used to predict temperature at 5 km depth in this area are simplistic and possibly do not give an accurate representation of the true distribution and magnitude of the temperature anomaly. Here we re-evaluate the geological controls on geothermal potential in the Queensland part of the temperature anomaly using a stochastic thermal model. The results illustrate that the temperature distribution is most sensitive to the thermal conductivity structure of the top 5 km. Furthermore, the results indicate the presence of silicic crust enriched in heat producing elements between and 40 km.

Innovative methods for assessing viability of diversification into new markets : a study based on an engineering consultancy

This study resulted in the development of a decision making tool for engineering consultancies looking to diversify into new markets. It reviewed existing decision tools used by contractor's entering new markets to develop a bespoke tool for engineering consultants to establish more rigor around the decision making process rather than rely purely on the intuition of company executives. The tool can be used for developing medium and long term company strategies or as a quick and efficient way to assess the viability of new market opportunities when they arise. A combination of Delphi and Analytical Hierarchy Process was selected as the basis of the decision theory.