Abstract: Financial markets have experienced a precipitous increase in complexity over the past decades, posing a significant challenge from a risk management point of view. This complexity motivates the application and development of sophisticated models based on the theory of stochastic...

Useful for mathematicians interested in the methods of modern mathematical finance without prior knowledge of advanced stochastic analysis, this book contains lecture notes which start with an elementary approach to stochastic calculus due to Follmer, who showed that one can develop Ito's...

Martingales and optimal stopping -- Derivatives in general and binomial markets -- Fundamental theorems of asset pricing -- Superhedging -- Hedging with risk -- Martingales in continuous time and optimal stopping -- Introduction to stochastic analysis -- Derivatives in the Black-Scholes market...