This important book provides information necessary for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty; introduces the reader to the main concepts, notions and results of stochastic financial mathematics; and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilistic and statistical ideas and the methods of stochastic calculus in the analysis of market risks.
Part 1 Facts. Part 2 Models: main concepts, structures and instruments; aims and problems of financial theory and financial engineering; stochastic models - discrete time; stochastic models - continuous time; statistical analysis of financial data. Part 3 Theory: theory of arbitrage in stochastic financial models - discrete time; theory of pricing in stochastic financial models - discrete time; theory of arbitrage in stochastic financial models - continuous time; theory of pricing in stochastic financial models - continuous time.