# FE710 Applied Stochastic Differential Equations

Course Catalog Description

# Introduction

Campus | Fall | Spring | Summer |
---|---|---|---|

On Campus | X | ||

Web Campus |

Instructors

Professor | Office | |
---|---|---|

Zhenyu Cui |
zcui6@stevens.edu | Babbio 514 |

More Information

# 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

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 |