Mathematical finance: theory review and exercises/ Emanuela Rosazza Gianin and Carlo Sgarra

Includes bibliography and index

Short review of probability and of stochastic processes -- Portfolio optimization in discrete time models -- Binomial model for option pricing -- Absence of arbitrage and completeness of market models -- Ito's formula and stochastic differential equations -- Partial differential equations in finance -- Black-Scholes model of option pricing and hedging strategies -- American options -- Exotic options -- Interest rate models -- Pricing models beyond Black-Scholes -- Risk measures: value at risk and beyond

The book is conceived as a guide to solve exercises in Mathematical Finance and a complement to theoretical lectures. The potential audience consists of students in Applied Mathematics, Engineering and Economics, attending courses in Mathematical Finance. The most important subjects covered by this textbook are Pricing and Hedging of different classes of financial derivatives (European, American Exotic options, Fixed Income derivatives) in the most popular modeling frameworks, both in discrete and continuous time setting, like the Binomial and the Black-Scholes models. A Chapter on static portfolio optimization, one on pricing for more advanced models and one on Risk Measures complete the overview on the main issues presented in classical courses on Mathematical Finance. About one hundred exercises are proposed, and a large amount of them provides a detailed solution, while a few are left as an exercise to the reader. Every chapter includes a brief resume of the main theoretical results to apply. This textbook is the result of several years of teaching experience of both the authors.