This book explains key financial concepts, mathematical tools and
theories of mathematical finance. It is organized in four parts. The
first brings together a number of results from discrete-time models. The
second develops stochastic continuous-time models for the valuation of
financial assets (the Black-Scholes formula and its extensions), for
optimal portfolio and consumption choice, and for obtaining the yield
curve and pricing interest rate products. The third part recalls some
concepts and results of equilibrium theory and applies this in financial
markets. The last part tackles market incompleteness and the valuation
of exotic options.