A complete set of the author’s lecture videos is available on YouTube, providing a comprehensive supplementary resource for a course or independent study. 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. Students should have experience with the standard calculus sequence, as well as a familiarity with differential equations and probability. Mathematics of Finance is ideal for undergraduates from a variety of backgrounds, including mathematics, economics, statistics, data science, and computer science. “Intuition breaks” frequently prompt students to set aside mathematical details and think critically about the relevance of tools in context. Throughout, the author presents topics in an engaging conversational style. Advanced topics that follow include the Greeks, American options, and embellishments. Omitting the mechanics of solving Black–Scholes itself, the presentation instead focuses on an in-depth analysis of its derivation and solutions. Chapters on modeling and probability lead into the centerpiece: the Black–Scholes equation. Introducing the basics of gambles through realistic scenarios, the text goes on to build the core financial techniques of Puts, Calls, hedging, and arbitrage. 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. 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. This amount is called the future value of P dollars at an interest rate r for time t in years. The interest, added to the original principal P, gives P + Prt P11 + rt2. 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. 200 ChAPTER 5 Mathematics of Finance A deposit of dollars today at a rate of interest P for years produces interest of t r I Prt.
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