Course: ORF 409
Instructor: William Massey
F 2017

Description of Course Goals and Curriculum

ORF 409 covers methods for simulating stochastic models in a wide variety of applications, including queuing, finance, and manufacturing. For example, you will calculate derivative prices based on simulations of underlying stocks. Or you will simulate behavior of queues under different arrival and service times. Monte Carlo simulation is a powerful method because many problems in practice do not lend themselves to closed-form mathematical solutions, but simulation allows us to still obtain precise answers and understanding of complex systems. ORF 409 proceeds linearly. First, there is a standard review of probability topics. Then, every week thereafter introduces a new simulation method or technique, with a focus towards the end of the course on analysis and variance reduction of simulation, two important factors when applying Monte Carlo methods in practice. The course is evenly balanced between theory and application, as problem sets and exams have both theoretical and computational components.  

Learning From Classroom Instruction


Lectures in ORF 409 are held twice per week for 80 minutes each lecture. Prof. Massey uses powerpoints for his lectures, and his lecture slides are very comprehensive. Lecture slides are posted online as well, so if a particular topic or derivation is covered too quickly in class, it’s a good idea and easy to review the topic after the fact. Lectures are focused on primarily on theory and derivations, with ost simulation specifics left for the textbook.

Assigned readings/texts

Prof. Massey follows the text for the class, “Simulation” by Sheldon Ross, very closely in his lectures. Homeworks are drawn from the textbook. Thus, the textbook is a valuable resource to reference when completing homeworks. If you don’t understand a topic as presented in lecture, you can reference the textbook for further explanation.  

Learning For and From Assignments


ORF 409 has problem sets due roughly every 1.5 weeks. Each problem set is closely related to that week’s lecture, and problems are drawn from the course textbook. The theory component on problem sets uses theorems and facts from lectures and textbooks to prove new results. The level and type of work in problem sets is very similar to exams, so it is as good idea to try to solve some problems on your own to gauge your understanding of the material. Students are encouraged to complete the computation questions using Python. The computation is the practical extension of the theory, and is quite useful for learning best practices of simulations. There are plenty of resources online for any Python issues, so as long as you have a familiarity with programming at the level of COS 126, ORF 409 computation problems will be quite accessible.


ORF 409 has two examinations: a take-home midterm and take-home final. These exams are very similar to homeworks in the class and contain a mix of theory and computation. The best preparation for these exams really is the homework. The exams are at a slightly higher difficulty than the homework problems. Theory questions often feature multiple parts, and computations are often significantly more involved. However, if you are successful solving homework problems mostly on your own, then you will find that with appropriate time allocation that exams are similarly manageable. As a take-home exam, the best preparation is to make sure you have a thorough understanding of material before the exam starts, as you are not allowed to use the internet or consult classmates when completing the take-home exam. Thus, use office hours and talking to others in the class before the exam to keep up with the material in class.  

External Resources

There is little need to use external resources for ORF 409. The lecture slides are comprehensive, and the textbook fills in any gaps in the lecture slides. The homeworks involve a considerable amount of coding in Python, so it is likely that you will use online documentation and resources for Python coding.

What Students Should Know About This Course For Purposes Of Course Selection

ORF 409 is an upper-level ORFE course that shows the practical application of statistics from ORF 245 and probability from ORF 309. For students interested in simulation work as a possibility for independent work, ORF 409 will be a valuable course that will teach the underlying principles of efficient simulation, and how to interpret uncertainty in simulation results. As a result, the course is broadly applicable for students in many disciplines. However, most students are ORFE majors or MFin students, so entering the class having taken ORF 309 and with an understanding of statistics at the level of ORF 245 would be beneficial.
Introduction to Monte Carlo Simulation

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