Mathematical Finance

In recent years the finance industry has mushroomed to become an important part of modern economies, and many science and engineering graduates have joined the industry as quantitative analysts, with mathematical and computational skills that are needed to solve complex problems of asset valuation and risk management. An important parallel story exists of scientific endeavour. Between 1965-1995, insightful ideas in economics about asset valuation were turned into a mathematical "theory of arbitrage," an enterprise whose first achievement was the famous 1973 Black-Scholes formula, followed by extensive investigations using all the resources of modern analysis and probability. The growth of the finance industry proceeded hand-in-hand with these developments. Now new challenges arise to deal with the fallout from the 2008 financial crisis and to take advantage of new technology, which has revolutionized the practice of trading.

This Very Short Introduction introduces readers with no previous background in this area to arbitrage theory and why it works the way it does. Illuminating pricing theory, Mark Davis explains its applications to interest rates, credit trading, fund management and risk management. He concludes with a survey of the most pressing issues in mathematical finance today.

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Mark Davis is Senior Research Fellow at the Department of Mathematics at Imperial College, London. Coming from a background in electrical engineering and computer science, with an ScD in Mathematics from Cambridge University, Professor Davis spent five years as Head of Research and Product Development at the London-based investment bank Tokyo-Mitsubishi International, before setting up a Mathematical Finance group at Imperial College London. He was awarded the Naylor Prize in Applied Mathematics by the London Mathematical Society in 2002. He is the author of six books, most recently Risk-Sensitive Investment Management (World Scientific 2014), written with Sebastien Lleo.