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This text covers the typical problems of continuous-time financial mathematics such as option pricing (in particular the Black-Scholes formula and corresponding variants) and portfolio optimization (determination of optimal investment strategies). Further, a separate chapter deals with exotic options and numerical methods. The required mathematical tools which include Brownian motion, Itô calculus, and stochastic control theory will be presented in self-contained excursions. The book is suitable as the basis of a course on financial mathematics building up on a basic course in probability.

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