This second edition - completely up to date with new exercises - provides a comprehensive and self-contained treatment of the probabilistic theory behind the risk-neutral valuation principle and its application to the pricing and hedging of financial derivatives. On the probabilistic side, both discrete- and continuous-time stochastic processes are treated, with special emphasis on martingale theory, stochastic integration and change-of-measure techniques. Based on firm probabilistic foundations, general properties of discrete- and continuous-time financial market models are discussed.

1 Derivative Background 2 Probability Background 3 Stochastic Processes in Discrete Time 4 Mathematical Finance in Discrete Time 5 Stochastic Processes in Continuous Time 6 Mathematical Finance in Continuous Time 7 Incomplete Markets 8 Interest Rate Theory 9 Credit Risk

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