Today probability turns out to be one of the most pervasive mathematical topics. It actually affects a number of quite different fields, proving particularly relevant to courses ranging from Statistics to Economics, from Finance to Management Science. Recently it has even found significant applications in some sectors of Law. This book contains a short presentation of the most basic aspects of probability theory. As a result, it should come in handy and help students grasp the main concepts of the discipline as well as acquire a basic probabilistic vocabulary, thus capturing at least the flavour of possible relevant applications. The book includes a sketch of von Neumann Đ Morgenstern utility theory, which is useful per se as well as being an enlightening bridge between probability and decision theories. The book also provides a substantial set of exercises with solutions.
The rewards and dangers of speculating in the modern financial markets have come to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investment. At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. Here now is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities. Key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model are described with mathematical precision in a style tailored for market practitioners. Starting from discrete-time hedging on binary trees, continuous-time stock models (including Black-Scholes) are developed. Practicalities are stressed, including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. A full glossary of probabilistic and financial terms is provided. This unique book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders.
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