Stochastic Calculus and Applications

Fall 2017, PSTAT 223A

Prerequisite to PSTAT 223B: Financial Modeling

Tu-Th 9:30-10:45 - HSSB 4202

	

Jean-Pierre Fouque

Office Hours: Wednesday 11:00--12:00 or by appointment

Office: South Hall 5504 fouque at pstat.ucsb.edu


Agenda:


Midterm exams: Tuesday October 24 and Tuesday November 21
Final exam: Tuesday December 12 (8-11am)

Week 1:

  • Thursday September 28: Brownian motion. Homework 1 due on Tuesday October 10: on pages 17-20: 2.8, 2.12, 2.13, 2.16, 2.17.

    Week 2:

  • October 3: Ito's integral (Chapter 3).
  • October 5: Ito's formula (Chapter 4). Homework 2 due on Tuesday October 17: on pages 37-42: 3.1, 3.4, 3.9, 3.18, and on pages 55-59: 4.1, 4.2, 4.5, 4.10, 4.11.

    Week 3:

  • October 10: Ito's formula (Chapter 4) continued.
  • October 12: Class given by Andrey Sarantsev: Stochastic Differential Equations (Chapter 5). Homework 3 due on Tuesday October 24: on pages 76-83: 5.1, 5.3, 5.5, 5.7, 5.11, 5.17, 5.18.

    Week 4:

  • October 17: Stochastic Differential Equations (Chapter 5) continued.
  • October 19: The filtering problem (Chapter 6).

    Week 5:

  • October 24: MIDTERM 1 (on Chapters 2 to 5) in class at 9:30AM, open documents.
  • October 26: The filtering problem (Chapter 6) continued. Homework 4 due on Tuesday November 7: 5.16, 6.2, 6.5, 6.8b + 6.9b (skip parts a; counts as a single question), 6.15

    Week 6:

  • October 31: Diffusions (Chapter 7).
  • November 2: Diffusions (Chapter 7) continued. Homework 5 due on Tuesday November 14: on pages 131-138: 7.1, 7.2, 7.4, 7.9, 7.18.

    Week 7:

  • November 7: Kolmogorov's backward and forward equations. Feynman-Kac formula. Resolvent (Chapter 8).
  • November 9: Chapter 8 continued. Homework 6 due on Tuesday November 21: on pages 171-175: 8.2, 8.5, 8.9, 8.10, 8.12, 8.13.

    Week 8:

  • November 14: Time change. Girsanov's transform (Chapter 8).
  • November 16: Girsanov's transform (Chapter 8) continued.

    Week 9:

  • November 21: MIDTERM 2 (on Chapters 6 to 8) in class at 9:30AM, open documents.
  • November 23: THANKSGIVING

    Course Outline

    An introduction to Brownian motion, stochastic calculus and stochastic differential equations. Diffusion processes, related partial differential equations and Feynman-Kac formula. Applications to filtering, stochastic control and mathematical finance.

    Prerequisites: PSTAT 213A-B-C (or equivalent first year graduate courses in Probability and Stochastic Processes.)

    Grading: Homework 30%, Midterms(2) 40%, Final 30%

    TEXT:
    Bernt Oksendal, Stochastic Differential Equations: An Introduction with Applications. Springer, 6th Edition (2003).