| Detail information of 'Aspects of Mathematical Finance' | |||||||||||||||||
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| The aim is to make these articles accessible to a wide audience belonging to scientific horizons; indeed, this half-day conference was attended by many young postgraduates in disciplines such as economics, management, and applied mathematics, along with many members of the different sections of the Acad´emie. Among the reasons to get interested in financial mathematics, the following is one: who has never wondered, looking at the financial pages of a newspaper, displaying the erratic evolutions of quotations on the Stock Exchange, if these were not “governed” by some models, likely to be probabilistic? This question was at the heart of the studies conducted by Louis Bachelier, particularly in his famous thesis (1900), and he answered the above question in terms of Brownian Motion. His remarkable results, however, remained in a kind of scientific limbo for almost 75 years, until Samuelson “corrected” Bachelier (in 1965) by replacing the BrownianMotion by its exponential, and the famous Black-Scholes formula began (in 1973) to play an essential role in the computation of option prices. Since the 1980s, we have witnessed the explosion of probabilistic models, along with financial products, each in turn becoming more and more complex. All this technology, which now forms an important part of financial engineering, exists only because some mathematical concepts both simple and universal allow building a “theory of the laws of markets,” based on principles such as the prices across time of an uncertain asset having the probabilistic structure of a fair game, that is to say of a martingale. From this concept, little by little was built the entire theory of stochastic processes, which is a pillar on which the mathematical theory of “arbitrage” was developed by Delbaen and Schachermayer. The six articles in this volume present the following main topics. click here to download the book | |||||||||||||||||
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