The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.

Parliamentary sovereignty, popular sovereignty, and Henry Parker's adjudicative standpoint

Discussions of popular sovereignty in early modern England have usually been premised upon a sharp distinction between ‘legal/constitutional’ forms of discourse (which merely interpret the law) and ‘political’ ones (which focus upon the right to make it). In such readings of the period, Henry Parker has a pivotal position as a writer who abandoned merely legalistic thinking. This chapter takes a different view. It argues that Parker’s major intellectual achievement was not so much to abandon legal/constitutional discourse as to offer a theorisation of its most distinctive features: he offered an account of a new kind of politics in which concern for ‘interests’ in property and in self-preservation replaced humanist concern with promotion of virtue. Parker drew upon ideas about representation best expressed by Sir Thomas Smith and ideas about law best expressed by Oliver St John. The theory he developed was not intended as a justification of legislative sovereignty, but of adjudicative supremacy. His picture of the two Houses as supreme adjudicators was meant to block the path to direct democracy. But the adjudicative standpoint they came to occupy presupposed that freeborn adults had ‘interests’ in life, liberty, and possessions. This had democratising implications.

The role of industry bodies in changing market practices through self-regulation: commercial property leasing in the UK

The UK government has sought to make changes to commercial property leasing practices. This has been the case since the recession of the 1990s. Industry self-regulation using an industry code of practice has been the vehicle for these changes. However, the code has had little direct success in changing practices. This is despite repeated threats of legislation as a constant backdrop to this initiative. The focus for this research is on the role of the industry bodies in the code initiative. They have been central to self-regulation in commercial leasing. Thus, the aim is to investigate the role of industry bodies in the process of institutional change. The context is industry self-regulation. The specific setting is commercial leasing. The main industry bodies in focus are the British Property Federation and Royal Institution of Chartered Surveyors. An existing model of institutional change forms the framework for the research. A chronological narrative is constructed from secondary data. This is analysed, identifying the actions of the industry bodies within the conceptual stages of the model. The analysis shows that the industry bodies had not acted as convincing agents of change for commercial leasing. In particular there was a lack of theorisation, a key stage in the process. The industry bodies did not develop a framework necessary to guide their members through the change process. These shortcomings of the industry bodies are likely to have contributed to the failure of the Code. However, the main conclusion is that, if industry self-regulation is led by government, then the state must work with industry bodies to harness their potential as champions and drivers of institutional change. This is particularly important in achieving change in institutionalised environments.

Location, location, location? Analysing property rents in medieval Gloucester

Although medieval rentals have been extensively studied, few scholars have used them to analyse variations in the rents paid on individual properties within a town. It has been claimed that medieval rents did not reflect economic values or market forces, but were set according to social and political rather than economic criteria, and remained ossified at customary levels. This paper uses hedonic regression methods to test whether property rents in medieval Gloucester were influenced by classic economic factors such as the location and use of a property. It investigates both rents and local rates (landgavel), and explores the relationship between the two. It also examines spatial autocorrelation. It finds significant relationships between urban rents and property characteristics that are similar to those found in modern studies. The findings are consistent with the view that, in Gloucester at least, medieval rents were strongly influenced by classical economic factors working through a competitive urban property market.