Kirjahaku

Finance provides a dramatic example of the successful application of advanced mathematical techniques to the practical problem of pricing financial derivatives. This self-contained 2002 text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus: proofs in the continuous-time world follow naturally. The Black-Scholes pricing formula is first derived in the simplest financial context. The second half of the book is then devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts can be applied to realistic financial questions.

Finance provides a dramatic example of the successful application of advanced mathematical techniques to the practical problem of pricing financial derivatives. This self-contained text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus: proofs in the continuous-time world follow naturally. The Black-Scholes pricing formula is first derived in the simplest financial context. The second half of the book is then devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts can be applied to realistic financial questions.

This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.