Preface to the first edition

This book is an introduction to probabilistic methods in Finance. It is intended for graduate students in mathematics, and it may also be useful for mathematicians in academia and in the financial industry. Our focus is on stochastic models in discrete time. This limitation has two immediate benefits. First, the probabilistic machinery is simpler, and we can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the discrete-time setting provides a shortcut to some of the more recent literature on incomplete financial ...

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