A securities market operator's use of the "please explain" price query and its impact on compliance

Market operators in New Zealand and Australia, such as the New Zealand Exchange (NZX) and the Australian Securities Exchange (ASX), have the regulatory power in their listing rules to issue queries to their market participants to explain unusual fluctuations in trading price and/or volume in the market. The operator will issue a price query where it believes that the market has not been fully informed as to price relevant information. Responsive regulation theory has informed much of the regulatory debate in securities laws in the region. Price queries map onto the lower level of the enforcement pyramid envisaged by responsive regulation and are one strategy that a market operator can use in communicating its compliance expectations to its stakeholders. The issue of a price query may be a precursor to more severe enforcement activities. The aim of this study is to investigate whether increased use of price queries by the securities market operator in New Zealand corresponded with an increase in disclosure frequency by all participating companies. The study finds that an increased use of price queries did correspond with an increase in disclosure frequency. A possible explanation for this finding is that price queries are an effective means of appealing to the factors that motivate corporations, and the individuals who control them, to comply with the law and regulatory requirements. This finding will have implications for both the NZX and the ASX as well as for regulators and policy makers generally.

A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction–diffusion equations

Fractional differential equations have been increasingly used as a powerful tool to model the non-locality and spatial heterogeneity inherent in many real-world problems. However, a constant challenge faced by researchers in this area is the high computational expense of obtaining numerical solutions of these fractional models, owing to the non-local nature of fractional derivatives. In this paper, we introduce a finite volume scheme with preconditioned Lanczos method as an attractive and high-efficiency approach for solving two-dimensional space-fractional reaction–diffusion equations. The computational heart of this approach is the efficient computation of a matrix-function-vector product f(A)bf(A)b, where A A is the matrix representation of the Laplacian obtained from the finite volume method and is non-symmetric. A key aspect of our proposed approach is that the popular Lanczos method for symmetric matrices is applied to this non-symmetric problem, after a suitable transformation. Furthermore, the convergence of the Lanczos method is greatly improved by incorporating a preconditioner. Our approach is show-cased by solving the fractional Fisher equation including a validation of the solution and an analysis of the behaviour of the model.

Insight into the fractional calculus via a spreadsheet

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.