Math 454   -    Financial Mathematics   -    Spring 2025  

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Last update: January 28, 2025 - 3:30 PM
NOTE that this document specifically pertains to Section 1 of the course!
Visit this page frequently for important changes and additions!


Course Material for Math 454

   
REQUIRED: Stochastic Calculus for Finance II - Continuous Time Models by Steven Shreve (Springer, 2004; ISBN 978-0-387-40101-0) (the "SCF2 text", also just "SCF2")
   
  1. I will strive to teach major portions of ch.1 through 6 from that book.
   
REQUIRED: Math 454 - Additional Material (lecture notes for the BU Math 454 course) by Michael Fochler, your instructor (the "MF454 notes" or simply "MF454").
   
  1. This document is work in progress and will be modified as the course unfolds.
  2. Almost all of the material in chapters 2 and 3 of this version is a straight copy from my Math 330 version 2020-11-28 lecture notes (see below).
  3. Most of ch. 4 (Basic Measure and Probability Theory) you will find neither there nor in the Shreve text, so you should Study that material.
  4. Older editions of the document will eventually be deleted. You can find them posted in reverse chronological order in this table:

    2025-01-26 version       Fixed some errors
    2025-01-17 version       Major rewrite of Ch.7, removal of Ch.8 (Financial Models - Part 1 OLD), lots of typos corrected in all chapters.
    Ch.1-6 are stable. The remaining ones might undergo substantial changes.
    2024-11-24 version     This is the first version of my Spring 2025 lecture notes for this course.
    There will be major corrections, some additions, and a reorganization of some of the material.
    At least one more release will be forthcoming before the start of the semester, so you are advised not to print any hardcopies yet!

   
Optional References:
   
  1. Brownian Motion Calculus by Ubbo F. Wiersema (Wiley, 2008)
  2. Stochastic Calculus for Finance I - The Binomial Asset Pricing Model by Steven Shreve (Springer, 2004)
  3. If you have some background in measure theoretical probability theory: Stochastic Differential Equations: An Introduction with Applications by Bernt Oksendal (Springer, 6th edition, 2003)
  4. Remedial Math: Probability Theory
    • Lecture Notes for Math 447 - Probability, by Michael Fochler (the "MF447 notes" or simply "MF447"). Review the following:
      1. ch.2-5, ch.11.7.
      2. ch.11 (except for ch.11.2.2 and 11.2.3).
      Here is a link to the 2024-11-24 version . It is the latest version for the Fall 2024 semester.
      For newer versions of the Math 447 lecture notes check my archive of all my lectures.
  5. Remedial Math: Sets, functions, equivalence relations, convergence and continuity, ...
    • The Art of Proof: Basic Training For Deeper Mathematics, by M. Beck and R. Geoghegan (Springer, 2010). You should review:
      1. chapters 5, 6.1, 9.1
    • Math 330 - Additional Material (lecture notes for the BU Math 330 course) by Michael Fochler (the "MF330 notes" or simply "MF330"). Review the following:
      1. ch. 2.1-2.3, ch.5, ch.8.1, 8.3, 8.4, ch.9.3,
      2. ch.11 (except for ch. 11.2.2 and 11.2.3).
      Here is a link to the 2024-11-25 version . It is the latest version for the Fall 2024 semester.
      For newer versions of the Math 330 lecture notes check my archive of all my lectures.
   
Additional Links
    The list below is likely to grow as the semester progresses.
   
  1. Solutions for selected quiz and exam problems:     •   Quiz 01 (quiz 1 solutions added on Jan 28)