Introduction

This course is designed for graduate students who took FE 610 and have a good grasp of understanding Probability and Stochastic Calculus. The objective is to understand Stochastic Differential Equations (SDE’s) both from theoretical and practical perspective

Course Description

TTopics include Ito calculus review, linear stochastic differential equations (SDE’s), examples of solvable SDE’s, weak and strong solutions, existence and uniqueness of strong solutions, Ito-Taylor expansions, SDE for Markov processes with jumps, Levy processes, forward and backward equtions and the Feynman-Kac representation formula, and introduction to stochastic control. Applications are mostly from fianncial engineering but applications in areas such as population dynamics, energy, climatology and seismology may also be presented. Prerequisites: FE 610, MA 611, MA 623

Textbook

We will provide notes additional to the textbook material. The main textbook used is:

Stochastic Differential Equation, by Bernt Øksendal, 6th edition, 2010, ISBN-10: 3540047581, ISBN-13: 978-3540047582 In addition the following textbooks provide additional references:

Additional References

• Stochastic Calculus for Finance vol I and II, by Steven E. Shreve,
Springer Finance, 2004, ISBN-13: 978-0387249681 (vol I) and 978-
1441923110 (vol II) (used in FE610).

• Eckhard Platen and Nicola Bruti-Liberati, Numerical Solutions of Stochas-
tic Differential Equations with Jumps in Finance, Springer 2010, ISBN:
978-3-642-12057-2

• Stochastic Calculus and Financial Applications, by J. Michael Steele,
Springer 2000, ISBN-10: 0387950168, ISBN-13: 978-0387950167

• Introduction to Stochastic Calculus With Applications by Fima C. Kle-
baner, , ISBN-10: 1848168322, ISBN-13: 978-1848168329

• Financial Calculus: An Introduction to Derivative Pricing by Martin
Baxter, Andrew Rennie, 1996, ISBN-10: 0521552893, ISBN-13: 978-
0521552899

• Introduction to the Mathemtics of Financial Derivatives, by Salih N
Neftci, 2nd ed, Associated Press, 2000, ISBN 0125153929.

• Handbook of Probability, by I. Florescu and C. Tudor, ISBN: 978-0-470-
64727-1, Oct. 2013. (for probability background)

• Probability and Stochastic Processes, by I. Florescu, ISBN: 978-0-470-
62455-5, Oct. 2014. (for both Probability and Stochastic processes
background)

Grading Policies

We will have several assignments throughout the course. We may have a midterm and/or final in the course. The percentage for all components will be decided and announced throughout the class.