# FE540 Probability theory for Financial Engineering

Course Catalog Description

# Introduction

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

On Campus | X | X | |

Web Campus | X | X |

Instructors

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

Ionut Florescu |
ifloresc@stevens.edu | Babbio 544 |

Course Resources

# Textbook

- [FT] Florescu, Ionut and Tudor, Ciprian A. Handbook of Probability, Wiley, 2014, ISBN 1118593146, 9781118593141.

I chose to use this book as the primary textbook for two reasons. Each chapter is supposed to be more or less self contained and it contains many details that I believe are useful. Second, each chapter has a section with exercises split into two, First set of problems have solutions while the second set does not. I will assign exercises that do not have solutions but you should be working through the ones that have solutions for practice. We will be using two other textbooks.

- [G] Ghahramani, Saeed Fundamentals of Probability: with Stochastic Processes, Third Edition, Chapman and Hill/CRC, Nov. 2015, ISBN 9781498755016

This is an undergraduate textbook and it is very useful for those of you who did not do a serious probability class in undergraduate. The book explains very well the basic probability distributions and concepts. I will be using exercises from the book and you should use it as a source of material and problems. Finally,

- [F] Florescu, Ionut Probability and Stochastic Processes, Wiley, Oct. 2014, ISBN-13: 978-0470624555, ISBN-10: 047062455

This book has more material than the main textbook but it isn’t as detailed which is why I am using the handbook as the main text. However, this book has a second part about stochastic processes which is I believe very useful for future. I am referring in particular to Markov chains and Markov processes, Poisson process and the Brownian motion.

Grading

# Grading Policies

Only use the .pdf format when submitting files online. If specified in class you can turn in handwritten assignment in the traditional way. You should be able to transform any document into a pdf file. You can use Adobe Acrobat - should be free to Stevens students as far as I know (please call the students help desk), or a simple alternative: use a pdf printer driver. I write all my documents in LATEX and that typesetting program produces pdf files. A simple alternative (using any typesetting program): search on google for a driver that would print to a pdf file. Such drivers are generally free. Late assignments will not be accepted under any circumstances without prior notice and permission of the instructor. If outside circumstances are affecting your ability to perform in the course, you must contact your instructor before you fall behind. Generally the grade distribution follows the following percentages.

### Grade distribution

Assignments: 30% Midterm: 25% Final: 40% Quizzes, class participation: 5%

Lecture Outline

Topic | Reading | |
---|---|---|

Week 1 | Axioms of Probability, Sample Spaces, Examples Combinatorial Analysis, Counting Permutations, Combinations, Binomial Coefficient | F-1, FT-1, G-1,2 |

Week 2 | Conditional Probability and Independence, Law of Total Probability, Bayes Theorem, Applications | FT-2, F-2, G-3 |

Week 3 | Random Variables: Generalities | FT-3 |

Week 4 | Discrete Random variables, examples | FT-4, G-4,5 |

Week 5 | Continuous Random variables, Examples | FT-5, G-6,7 |

Week 6 | Generating Random variables. Catching up. | FT-6, F-3 |

Week 7 | MIDTERM | |

Week 8 | Random vectors, Joint distribution | FT-7, F-4 |

Week 9 | Conditional distribution, Conditional expectation | G-8,9 |

Week 10 | Moment Generating Function, Characteristic Function | FT-8,9,F-6 |

Week 11 | Gaussian Random Vectors, Catch up | FT-10 |

Week 12 | Statistical Inference, Limit Theorems | FT-11,12, F-7,8 |

Week 13 | Poisson Process and Markov Chain | F-10,12 G-12.2,12.4 |

Week 14 | Brownian motion | F-15, G-12.5 |