This book gives a systematic introduction to the basic theory of
financial mathematics, with an emphasis on applications of
martingale methods in pricing and hedging of contingent claims,
interest rate term structure models, and expected utility
maximization problems. The general theory of static risk measures,
basic concepts and results on markets of semimartingale model, and
a numeraire-free and original probability based framework for
financial markets are also included. The basic theory of
probability and Ito's theory of stochastic analysis, as preliminary
knowledge, are presented.
General
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