Time domain decomposition for European options in financial modelling

Finance is one of the fastest growing areas in modern applied mathematics with real world applications. The interest of this branch of applied mathematics is best described by an example involving shares. Shareholders of a company receive dividends which come from the profit made by the company. The proceeds of the company, once it is taken over or wound up, will also be distributed to shareholders. Therefore shares have a value that reflects the views of investors about the likely dividend payments and capital growth of the company. Obviously such value will be quantified by the share price on stock exchanges. Therefore financial modelling serves to understand the correlations between asset and movements of buy/sell in order to reduce risk. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. There are other financial activities and it is not an intention of this paper to discuss all of these activities. The main concern of this paper is to propose a parallel algorithm for the numerical solution of an European option. This paper is organised as follows. First, a brief introduction is given of a simple mathematical model for European options and possible numerical schemes of solving such mathematical model. Second, Laplace transform is applied to the mathematical model which leads to a set of parametric equations where solutions of different parametric equations may be found concurrently. Numerical inverse Laplace transform is done by means of an inversion algorithm developed by Stehfast. The scalability of the algorithm in a distributed environment is demonstrated. Third, a performance analysis of the present algorithm is compared with a spatial domain decomposition developed particularly for time-dependent heat equation. Finally, a number of issues are discussed and future work suggested.

Resulting trusts, joint borrowers and beneficial share

Reviews case law illustrating the courts' approach to beneficial ownership of property purchased in joint name by means of a joint mortgage but without any declaration of beneficial interest, the resulting trust and joint beneficial interest presumptions. Contrast the approach adopted in cases where one party made no contribution to the mortgage payments with those where both parties made a contribution. Highlights the courts' treatment of the right to buy discount afforded tenant purchasers and property purchased as a commercial venture rather than a home.

Paying the price for loss of light

Considers the Court of Appeal ruling in Forsyth-Grant v Allen on the principles to be applied in assessing damages for the loss of light. Outlines the method for calculating damages for loss of right to light, the type of amenity which will be included in calculations for loss of amenity and the process applied in this case for assessing damages arising from the loss of profits that would have been made by the owner of the right to light if they had negotiated to relax the covenant, with reference to case law. Notes the limits to damages available for hypothetical loss and the difference between this award of profits and an account of profits.

A price worth paying?: Women and work – choice, constraint or satisficing

Purpose – Are women held back or holding back? Do women choose their jobs/careers or are they structurally or normatively constrained? The purpose of this paper is to shed fresh light on these questions and contribute to an on-going debate that has essentially focused on the extent to which part-time work is women’s choice, the role of structural and organisational constraints and the role of men in excluding women. Design/methodology/approach – The paper uses data from interviews with 80 working women – both full-time and part-time – performing diverse work roles in a range of organisations in the south east of England. Findings – It was found that many women do not make strategic job choices, rather they often ‘‘fall into’’ jobs that happen to be available to them. Some would not have aspired to their present jobs without male encouragement; many report incidents of male exclusion; and virtually all either know or suspect that they are paid less than comparable men. Those working reduced hours enjoy that facility, yet they are aware that reduced hours and senior roles are seen as incompatible. In short, they recognise both the positive and negative aspects of their jobs, whether they work full or part-time, whether they work in male-dominated or female-dominated occupations, and whatever their position in the organisational hierarchy. Accordingly, the paper argues that the concept of ‘‘satisficing’’, i.e. a decision which is good enough but not optimal, is a more appropriate way to view women’s working lives than are either choice or constraint theories. Originality/value – There is an ongoing, and often polarised, debate between those who maintain that women choose whether to give preference to work or home/family and others who maintain that women, far from being self-determining actors, are constrained structurally and normatively. Rather than supporting these choice or constraint theories, this paper argues that ‘‘satisficing’’ is a more appropriate and nuanced concept to explain women’s working lives.

Cohabitation: quantifying an equitable share

Discusses the House of Lords judgment in Stack v Dowden on the factors the courts may consider when determining whether to rebut the presumption that former cohabitees, who were registered as joint legal owners of a property, were also joint beneficial owners with equal shares in the property. [From the Legal Journals Index]

Memorandum submitted by the University of Greenwich: are the consumer price increases for electricity imposed in January 2008 justified?

This paper examines whether increases to published wholesale prices justify the retail electricity price increases imposed on residential consumers in January 2008. The study is based on analysis of two questions: Is the reported wholesale price a reliable indicator of the cost electricity retailers are paying to buy power; and is the corporate structure of the British electricity sector competitive? [Taken from first paragraph of summary]