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.
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