Financial mathematics. The evaluation of derivatives. (Q444621)

The textbook at hand is an introduction to the field that has become known as ``mathematical finance''. In particular, it deals with the pricing and hedging of derivative securities, both in discrete- and in continuous-time models. The book grew out of a two-semester course only assuming knowledge in probability theory, and therefore develops the required mathematical tools from stochastic calculus in a self-contained manner. The selection is tailored to the needs of the financial applications, but the presentation is mathematically rigorous throughout. On the mathematical side, topics covered include martingale theory, stochastic integration, and stochastic differential equations. As for financial problems, the book focuses on the pricing and hedging of derivative securities by arbitrage arguments, but also contains introductions to interest rate models as well as incomplete markets with stochastic volatilities and price jumps. Each chapter contains a set of exercises.