An investigation of innovation and knowledge creation in virtual worlds

The Internet and World Wide Web have had, and continue to have, an incredible impact on our civilization. These technologies have radically influenced the way that society is organised and the manner in which people around the world communicate and interact. The structure and function of individual, social, organisational, economic and political life begin to resemble the digital network architectures upon which they are increasingly reliant. It is increasingly difficult to imagine how our ‘offline’ world would look or function without the ‘online’ world; it is becoming less meaningful to distinguish between the ‘actual’ and the ‘virtual’. Thus, the major architectural project of the twenty-first century is to “imagine, build, and enhance an interactive and ever changing cyberspace” (Lévy, 1997, p. 10). Virtual worlds are at the forefront of this evolving digital landscape. Virtual worlds have “critical implications for business, education, social sciences, and our society at large” (Messinger et al., 2009, p. 204). This study focuses on the possibilities of virtual worlds in terms of communication, collaboration, innovation and creativity. The concept of knowledge creation is at the core of this research. The study shows that scholars increasingly recognise that knowledge creation, as a socially enacted process, goes to the very heart of innovation. However, efforts to build upon these insights have struggled to escape the influence of the information processing paradigm of old and have failed to move beyond the persistent but problematic conceptualisation of knowledge creation in terms of tacit and explicit knowledge. Based on these insights, the study leverages extant research to develop the conceptual apparatus necessary to carry out an investigation of innovation and knowledge creation in virtual worlds. The study derives and articulates a set of definitions (of virtual worlds, innovation, knowledge and knowledge creation) to guide research. The study also leverages a number of extant theories in order to develop a preliminary framework to model knowledge creation in virtual worlds. Using a combination of participant observation and six case studies of innovative educational projects in Second Life, the study yields a range of insights into the process of knowledge creation in virtual worlds and into the factors that affect it. The study’s contributions to theory are expressed as a series of propositions and findings and are represented as a revised and empirically grounded theoretical framework of knowledge creation in virtual worlds. These findings highlight the importance of prior related knowledge and intrinsic motivation in terms of shaping and stimulating knowledge creation in virtual worlds. At the same time, they highlight the importance of meta-knowledge (knowledge about knowledge) in terms of guiding the knowledge creation process whilst revealing the diversity of behavioural approaches actually used to create knowledge in virtual worlds and. This theoretical framework is itself one of the chief contributions of the study and the analysis explores how it can be used to guide further research in virtual worlds and on knowledge creation. The study’s contributions to practice are presented as actionable guide to simulate knowledge creation in virtual worlds. This guide utilises a theoretically based classification of four knowledge-creator archetypes (the sage, the lore master, the artisan, and the apprentice) and derives an actionable set of behavioural prescriptions for each archetype. The study concludes with a discussion of the study’s implications in terms of future research.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.