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Aimed at those who need to understand the mathematics behind the multitude of current financial instruments used in derivative markets, including risk managers and other practitioners§Begins with the mathematics used in discrete-time models, which can be more simply explained, then moves into the more difficult continuous-time models Includes detailed analyses of the famous§Black-Scholes theory, American put options, term structure models, and consumption-investment problems§Provides a clear understanding of pricing and hedging for call and put options§The mathematics used is accessible§The mathematics of martingales and stochastic calculus is developed where needed§The treatment is careful and detailed rather than comprehensive