Financial Mathematics

Modern financial mathematical methods are closely linked to the theory of stochastic processes. Concepts and results from this theory, including stochastic integration, are presented in this textbook in relation to financial economic issues. Based on prior knowledge of probability theory, the reader is introduced to the essential methods for analyzing and valuing financial derivatives, thereby gaining a deeper understanding of the practice of financial markets. Newly included are the theory of incomplete markets and stochastic volatility models, as well as the representation of jump processes and market models with jumps.

The content:

• Introduction to price theory
• Stochastic foundations of discrete markets
• Price theory in the n-period model
• American claims and optimal stopping
• The fundamentals.