Arbitrage Theory provides the foundation for the pricing of financial derivatives and has become indispensable in both financial theory and financial practice. This textbook offers a rigorous and comprehensive introduction to the mathematics of arbitrage pricing in a discrete-time, finite-state economy in which a finite number of securities are traded. In a first step, various versions of the Fundamental Theorem of Asset Pricing, i.e., characterizations of when a market does not admit arbitrage opportunities, are proved. The book then focuses on incomplete markets where the main concern is to obtain a precise description of the set of “market-consistent” prices for nontraded financial contracts, i.e. the set of prices at which such contracts could be transacted between rational agents. Both European-type and American-type contracts are considered. A distinguishing feature of this book is its emphasis on market-consistent prices and a systematic description of pricing rules, also at intermediate dates. The benefits of this approach are most evident in the treatment of American options, which is novel in terms of both the presentation and the scope, while also presenting new results. The focus on discrete-time, finite-state models makes it possible to cover all relevant topics while requiring only a moderate mathematical background on the part of the reader. The book will appeal to mathematical finance and financial economics students seeking an elementary but rigorous introduction to the subject; mathematics and physics students looking for an opportunity to get acquainted with a modern applied topic; and mathematicians, physicists and quantitatively inclined economists working or planning to work in the financial industry.

My original intention in writing this book was to consider evolving mar­ ket systems and Hayekian criteria of efficiency (see von Hayek (1931, 1945) ), and to discover those formal structures which might possibly lie at the base of economic systems capable of evolution. Much work in this field had already been done by others (see, for example, Kirzner (1975) and Nelson/Winter (1982) ), and a consensus seems to have been reached that something like system theory must be the logical point of departure for evolutionary theory in economics. But most of the previous work in this area is purely intuitive, and though there is much talk in it of systems and system theory, a precise definition of the concept of a system in this context is nowhere to be found. I had hoped to be able to sketch a working definition of pricing and production systems in a few pages and then to go on to investigate their performance within the framework of modern stability analysis. It soon became clear, however, that difficult and complex problems arise from the very outset of such an endeavor. If, for example, one speaks of dynamic systems of pricing and production, it should be made clear just how these systems differ from those portrayed in standard price theory and why that theory is inadequate for such analysis.

This Palgrave Pivot reviews the history of the UK's Retail Prices Index (RPI) from its origins just after the Second World War to its controversial position today. Both the developments in the methodology of the index and the political and social context in which its development took place are closely examined. The authors explain how the RPI went from being the dominant measure of inflation for decades to its current position as an officially discredited index. Despite this status, it is still widely used and attracts much support from a range of stakeholders, including several areas of government. Important reading for anyone interested in both sides of the argument for and against RPI and the likely way forward for the measurement of inflation.

Nick Mayhew has made key contributions to fields as diverse as medieval European monetary history, numismatics, financial history, price and wage history, and macroeconomic history. These essays, in his honour, demonstrate the analytical power and chronological reach of the novel interdisciplinary approach he has nurtured in himself and others.

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