Book DescriptionThis book is an introduction to financial mathematics for mathematicians It is intended both for graduate students with a certain background in probability theory as well as for professional mathematicians in industry and academia In contrast to many textbooks on mathematical finance, only discrete-time stochastic models одйнж are considered This setting has the advantage that the text can concentrate from the beginning on typical problems which are suggested by financial applications Moreover, certain principles, such as the general incompleteness of realistic market models, become thus more transparent and visible On the other hand, all models are based on general probability spaces, and so the text captures the interplay between probability theory and functional analysis which is typical for modern mathematical finance The first part of the book contains a study of financial investments in a static one-period market model Here, an investor faces intrinsic risk and uncertainty, which cannot be hedged away The tools presented to deal with this situation range from the classical theory of expected utility until the more recent development of measures of risk In the second part of the book, the idea of dynamic hedging and arbitrage-free pricing of contingent claims is developed in a multi-period framework Such market models are typically incomplete, and particular focus is given to methods combining the dynamic hedging of a risky position with the tools of assessing risk and uncertainty as presented in part Contents: Mathematical finance in one period: Arbitrage theory Expected utility Optimal investments Measures of risk Dynamic Arbitrage Theory: Dynamic hedging of contingent claims American contingent claims Optional decomposition and super-hedging Efficient hedging in incomplete markets Minimizing the hedging error Hedging under constraints References Index.  Паззл Карта2004 г ISBN 3110183463.