EAN: 9783030254421

UNDERGRADUATE TEXTS IN MATHEMATICS MATHEMATIC...

This textbook invites the reader to develop a holistic grounding in mathematical finance  where
concepts and intuition play as important a role as powerful mathematical tools. Financial
interactions are characterized by a vast amount of data and uncertainty  navigating the
inherent dangers and hidden opportunities requires a keen understanding of what techniques to
apply and when. By exploring the conceptual foundations of options pricing  the author equips
readers to choose their tools with a critical eye and adapt to emerging challenges. Introducing
the basics of gambles through realistic scenarios  the text goes on to build the core financial
techniques of Puts  Calls  hedging  and arbitrage. Chapters on modeling and probability lead
into the centerpiece: the Black-Scholes equation. Omitting the mechanics of solving
Black-Scholes itself  the presentation instead focuses on an in-depth analysis of its
derivation and solutions. Advanced topics that follow include the Greeks  American options  and
embellishments. Throughout  the author presents topics in an engaging conversational style.
Intuition breaks frequently prompt students to set aside mathematical details and think
critically about the relevance of tools in context. Mathematics of Finance is ideal for
undergraduates from a variety of backgrounds  including mathematics  economics  statistics 
data science  and computer science. Students should have experience with the standard calculus
sequence  as well as a familiarity with differential equations and probability. No financial
expertise is assumed of student or instructor  in fact  the text's deep connection to
mathematical ideas makes it suitable for a math capstone course. A complete set of the author's
lecture videos is available on YouTube  providing a comprehensive supplementary resource for a
course or independent study.

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