Math 574 Applied Optimal Control
with emphasis on the control of jumpdiffusion stochastic processes
for Fall 2006 (see Text).
Professor Emeritus F. B. Hanson (hanson at uic dot edu, 705 SEO, x33041)
Time Table:
25363 LCD 04000450PM M W F 205 LH
Lecturer: F. B. Hanson, 507 SEO, please use email (X63041msg)
 EMail: hanson at uic dot edu
 Web Page:
http://www.math.uic.edu/~hanson/
 Class Web Page (this page): http://www.math.uic.edu:~hanson/math574/
 Office Hours: Please make arrangements for
 3:253:50PM MWF 507 SEO
AND/OR
 4:505:15PM MWF 205 LH
Catalog description:
Introduction to optimal control theory;
calculus of variations, maximum principle, dynamic programming, feedback
control, linear systems with quadratic criteria, singular control,
optimal filtering, stochastic control.
Fall 2006:
During this semester, the course
will emphasize stochastic processes and control for jumpdiffusions
with applications to computational finance.
See the final draft text of Hanson, to be published in SIAM
Books Advances in Design and Control Series, for the class, including a
background online Appendix B Preliminaries, that can be used for prerequisites.
Prerequisites: Graduate standing AND Math 411 Advanced Calculus II
or Math 427 Analysis in Several Variables or consent of the instructor.
(See also online Appendix B Preliminaries.)
Comments: This course is strongly recommended for students in
Applied and Financial Mathematics since
it illustrates important application areas. The course is used to prepare
Doctoral students interested in Mathematical Control, Information
Theory, Applied Probability, Optimization, Computational Finance or
Financial Engineering, Mathematical Biology, Mathematical Medicine and
general Applied Mathematics.
Approximate List of Topics:  Hours:
 Introduction to JumpDiffusion Stochastic Differential Equations
(Chapters 0104 with online Appendix B where needed).  10 hours.
 SpaceTime Jump Processes and MultiDimensional SDEs
(Chapter 05).  6 hours.
 Deterministic Optimal Control.  5 hours.
 Stochastic Optimal Control and Dynamic Programming.  6 hours.
 Forward and Backward Kolmogorov Equations.  3 hours.
 Applications to Financial Engineering.  5 hours.
 Applications to Biomedicine.  2 hours.
 Computational Methods for Stochastic Dynamic Programming.  3 hours.
 Abstract Approaches: Martingales and Levy Processes.  3 hours.
 Leeway.  2 hours.
 Total.  45 hours.
Text:


Floyd B. Hanson,
Applied Stochastic Processes and Control for JumpDiffusions:
Modeling, Analysis, and Computation,
SIAM Books: Advances in Design and Control Series,
Order Code DC13,
published 03 October 2007,
28 + 441 pages, plus online appendices and sample codes.
(There is always a 30% off for members and complementary student
membership is available at many institutions. In Europe and Asia, the
book can be found, but without SIAM membership discount, at
Cambridge University Press.)

Optional or Supplementary Texts and Other References:
 D. E. Kirk, Optimal Control Theory: An Introduction, PrenticeHall,
1970. (former textbook on deterministic control, Dover reprinted 2004).
 R. F. Stengel, Optimal Control and Estimation, Dover Paperback, 1994
(About $18 including shipping at www.amazon.com, better choice for a
text book for stochastic control part of course).
 A. E. Bryson and Y. C. Ho, Applied Optimal Control,
Hemisphere/Wiley, 1975. (older, former textbook).
 B. D. O. Anderson and J. B. Moore, Optimal Control, PrenticeHall,
1990.
 T. Mikosch, Elementary Stochastic Calculus with Finance in View,
1998. (elementary, but abstract, introduction to Brownian motions or
Wiener processes).
 B. Øksendal, Stochastic Differential Equations:
An Introduction with
Applications, 1998. (elementary, but still quite abstract, introduction to
Brownian motions or Wiener processes).
 Z. Schuss, Theory and Applications of Stochastic Differential Equations,
1980. (introduction to both white and colored stochastic processes).
 D. L. Snyder and M. I. Miller,
Random Point Processes in Time and Space, 2nd edition, SpringerVerlag,
New York, NY, 1991.
(more advanced Poisson process reference).
Other references:
 L. Arnold, Stochastic Differential Equations: Theory and
Applications, 1974. (introduction to Wiener or diffusion processes).
 E. Çinlar, Introduction to Stochastic Processes, 1975. (good
introduction to Poisson processes).
 Peter Dorato, Chaouki Abdallah (Contributor) and Vito Cerone
(Contributor)
LinearQuadratic Control : An Introduction,
Prentice Hall, ISBN: 0023299622 (www.amazon.com price: $42.00)

Future Directions in Control in an Information
Rich World: Report of the Panel on Future Directions
in Control, Dynamics, and Systems, R. M. Murray (Editor), Society
for Industrial and Applied Mathematics, Philadelphia, PA, July
2003.
 P. Glasserman,
Monte Carlo Methods in Financial Engineering,
SpringerNY, New York, NY, 2003.

Floyd B. Hanson,
Computational Stochastic Control: Basic Foundations, Complexity and
Techniques,
Proceedings of 2003 Conference on Decision and Control,
pp. 30243029, Invited Poster/Interactive Paper in a Control Education
Session, 912 December 2003.

Floyd B. Hanson,
Techniques in Computational Stochastic Dynamic Programming,
in Stochastic Digital Control System Techniques,
within series Control and Dynamical Systems: Advances in Theory
and Applications,
vol. 76, (C. T. Leondes, Editor), Academic Press, New York, NY,
pp. 103162, Invited Book Chapter, April 1996.
 F. B. Hanson et al.,
Computational Stochastic Dynamic Programming Papers,
including applications to bioeconomics, groundwater remediation,
manufacturing, etc.
 F. B. Hanson et al.,
Computational Finance Papers, including optimal portfolio
and market parameter estimation papers.
 F. B. Hanson et al.,
Stochastic Biomedical Papers, including extinction/disaster,
fisheries harvesting, cancer, neurophysiology, etc. model papers.
 D. J. Higham,
An Introduction to Financial Option Valuation: Mathematics,
Stochastics and Computation,
Cambridge University Press, Cambridge, UK, 2004.
 Desmond J. Higham and Nicolas J. Higham,
MATLAB Guide, SIAM, 2000.
 J. C. Hull,
Options, Futures, & Other Derivatives, 4th Edition,
PrenticeHall, Englewood Cliffs, NJ, 2000.
 P. Jäckel,
Monte Carlo Methods in Finance,
John Wiley, New York, NY, 2002.
 S. Karlin and H. M. Taylor,
A First Course in Stochastic Processes,
2nd ed., Academic Press, New York, NY, 1975.
 S. Karlin and H. M. Taylor,
A Second Course in Stochastic Processes,
Academic Press, New York, NY, 1981.
 P. E. Kloeden and E. Platen,
Numerical Solution of Stochastic Differential Equations,
SpringerVerlag, New York, NY, 1999.
 H. J. Kushner and P. G. Dupuis,
Numerical Methods for Stochastic Control Problems in Continuous Time,
2nd ed., SpringerVerlag, New York, NY, 2001
 A. Lipton,
Mathematical Methods for Foreign Exchange: A Financial Engineer's
Approach, World Scientific, Singapore, 2001.
 J. M. Steele,
Stochastic Calculus and Financial Applications,
SpringerNY, New York, NY, 2001.
 S. Stojanovic,
Computational Financial Mathematics using MATHEMATICA:
Optimal Trading in Stocks and Options,
Birkhäuser, Boston, MA, 2002.
 H. M. Taylor and S. Karlin,
An Introduction to Stochastic Modeling,
3rd ed., Academic Press, New York, NY, 1998.
(Karlin and Taylor, "A Third Course".)
 H. C. Tuckwell,
Elementary Applications of Probability Theory,
Chapman and Hall, London, UK, 1995.
 P. Wilmott,
Paul Wilmott on Quantitative Finance, vols. 1 & 2,
John Wiley, New York, NY, 2000.
 Harry (Hui) Cheng, Ch AllInOne Language System,
An free
alternative, for academic use, to MATLAB and Numerical Recipes, is the
Ch Language System which combines the benefits of Unix, C and
MATLABclone in one complete selfcontained package for MSwindows and
other operating systems. It is free for academic use, see the webpage
Download
Ch
(Developed by Prof. Harry Cheng of UC/Davis; he is a UIC Ph.D. in ME,
Gupta and Hanson were his primary and secondary advisors).
Grade Policy:
Based on Individual Homework. Grades discounted if work to similar.
Class Homework Assignments
(to be updated for Fall 2006)
:
Class Notes:
Control Tools
Web Source: http://www.math.uic.edu/~hanson/math574/
Email Comments or Questions to
hanson at uic dot edu