FE710 Applied Stochastic Differential Equations

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Course Catalog Description

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.
Campus Fall Spring Summer
On Campus X X
Web Campus

Instructors

Professor Email Office
Zhenyu Cui
zcui6@stevens.edu Babbio 514



More Information

Course Description

Topics 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



Course Resources

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

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.


Lecture Outline

Topic Reading
Week 1 Introduction to Financial Engineering Ch. 1 and 2
Week 2 Capital Markets Overview Ch. 3
Week 3 Corporate Finance & Valuation Ch. 3
Week 4 Equity Analysis Ch. 4
Week 5 Fixed Income Debt Securities Ch. 4
Week 6 Overview of Bonds Sectors & Instruments Ch. 4
Week 7 Valuation of Debt Securities Ch. 4
Week 8 Securitized Products
Week 9 Leveraged Loans & CLO's Ch. 5
Week 10 General Principles of Credit Analysis Ch. 5
Week 11 Foreign Exchange Ch. 6
Week 12 Poisson Processes and Jump Diffusion Ch. 11
Week 13 Exotic Options Ch. 7
Week 14 Review & Catch-up