Stochastic Calculus and Applications

Fall 2018, PSTAT 223A

Prerequisite to PSTAT 223B: Financial Modeling

Tu-Th 9:30-10:45 - GIRV 2120

	

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 23 and Tuesday November 27
Final exam: Tuesday December 11 (8-11am)

Week 1:

  • Thursday September 27: Brownian motion. Homework 1 due on Tuesday October 9: on pages 17-20: 2.8, 2.12, 2.13, 2.16, 2.17.

    Week 2:

  • October 2: Ito's integral (Chapter 3).
  • October 4: Ito's formula (Chapter 4). Homework 2 due on Tuesday October 16: 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 9: Ito's formula (Chapter 4) continued.
  • October 11: Stochastic Differential Equations (Chapter 5). Homework 3 due on Tuesday October 23: on pages 76-83: 5.1, 5.3, 5.5, 5.7, 5.11, 5.17, 5.18.

    Week 4:

  • October 16: Stochastic Differential Equations (Chapter 5) continued.
  • October 18: The filtering problem (Chapter 6).

    Week 5:

  • October 23: MIDTERM 1 (on Chapters 2 to 5) in class at 9:30AM, open documents.
  • October 24: The filtering problem (Chapter 6) continued. Homework 4 due on Tuesday November 6: 5.16, 6.2, 6.5, 6.8b + 6.9b (skip parts a; counts as a single question), 6.15

    Week 6:

  • October 30: Diffusions (Chapter 7).
  • November 1: Diffusions (Chapter 7) continued. Chapter 8. Homework 5 due on Tuesday November 13: on pages 131-138: 7.1, 7.2, 7.4, 7.9, 7.18.

    Week 7:

  • November 6: Chapter 8. Time change. Girsanov Theorem.
  • November 8: Chapter 8 continued. Homework 6 due on Tuesday November 20: on pages 171-175: 8.2, 8.5, 8.9, 8.10, 8.12, 8.13.

    Week 8:

  • November 13: Optimal stopping.
  • November 15: Optimal stopping continued.

    Week 9:

  • November 20: Stochastic control.
  • November 22: THANKSGIVING

    Week 10:

  • November 27: MIDTERM 2 (on Chapters 6 to 8) in class at 9:30AM, open documents.
  • November 29: NO CLASS.

    Week 11:

  • December 4: Stochastic control.
  • December 6: Stochastic control (continued).

    Final Week:

  • Final exam: Tuesday December 11 (8-11am)

    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).