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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.

This report was jointly launched by the National Academy of Economic Strategy of the Chinese Academy of Social Sciences and UN-HABITAT. Using the indicator system and objective data, the competitiveness of 1,035 global cities was evaluated in detail. The report measures the development pattern of global urban competitiveness as a whole, and the gap between the relevant parties and the ideal state. It has refreshed people's past perceptions of urban rankings and confirmed that the science and technology innovation center cities and central cities of emerging economies have begun to break the inherent global cities and they have entered the ranks of the most urban competitiveness. While paying attention to the comparison of competitiveness among cities, this report further promotes the perspective to the pattern and trend change of global economic and social development from the perspective of city. The followings are new findings: First, information technology has increasingly become the primary driving force for urban development; Second, it is the three meridians that divide the global urban population and economic differentiation; Third, the soft links between cities gradually dominate the global urban system; Fourth, the formation of new global cities is beginning.

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