# Mathematics and Finance

### TW-Mi-187

**The financial crises of the past decade have shown financial markets to be very dynamic, affecting many aspects of our lives. And that there is a growing demand for people with insight in financial mathematical models and their suitability to model aspects of the (financial) world. **

The breadth, width, and diversity, of products, processes, and regulations in the financial world is staggering and quantitative models are everywhere and play a dominant role. So, both knowledge of this world and insight and skill regarding these models are necessary to participate in this world. This is too much to cover in one minor program. What is possible is this: introduce you to some important areas of finance and at the same time create an opportunity to find out what it would take to go deeper into the field of mathematics (perhaps specializing in Financial Engineering, but not necessarily).

Specifically, in this minor you encounter the three core courses from the minor Finance as well as a more rigorous mathematics course named *Probability for Finance*, a bit like you might find in the master Applied Mathematics and which requires the course *Mathematical Structures *as preparation*. *To be frank, the course is more probability than finance, and this is because if you want to truly understand some of the models used in finance, some deep and fundamental mathematics is needed: more and deeper than you are used to. So, doing these courses you can prepare yourself a bit (in case you want to continue in math) and find out what studying mathematics or mathematical finance would entail and whether you like that or not. It is a selection minor because it is a demanding minor and we want to ensure as much as we can that those who take it do this for the right reasons and have a high probability to succeed.

**Faculty of Electrical Engineering, Mathematics & Computer Science**

**ECs:** 30

**Language:** English

**Minimum participants:** 10

**Maximum participants: **30

Non-selection minor: | |

Selection minor: | |

Criteria: Superior performance on mathematics courses, especially probability and statistics (as evidenced through SVO) and motivation for and interest in mathematics (as demonstrated through motivation letter; details specified under How to register). |

### Education methods

Lectures, exercises, computer exercises, projects### Participating institutions

Faculty of Electrical Engineering, Mathematics & Computer Science### For whom?

This is not a more mathematical version of the minor Finance: if your main interest is finance, and you only consider the mathematics involved as a useful and sometimes necessary tool, then you should definitely choose the minor Finance.

However, the more you are inclined to confirm the following statements, the more this is an indication that the minor Mathematics and Finance may be for you:

- “There is some chance that I would like to do a master in mathematics.”
- “When I was learning to apply mathematics, I was often bothered by the fact that they did not tell us why this is a correct way to do things.”

The minor is intended for students from LR, WB, MT, TN, MST, TI, EE, and TW (but see note below), provided they possess ample prerequisite skills, good knowledge of and strong skills in mathematics, and enthusiasm for abstract mathematics (details: see selection criteria and *How to register*). Specifically required: probability and statistics at the level of TU courses based on *A Modern Introduction to Probability and Statistics *by Dekking et al, or equivalent. We expect you to be able to solve three quarters of the problems from the book, and not just simple computational exercises but also the insight ones.

* Note for TW students:* Mathematical Structures is part of the BSc programme Applied Mathematics, and for TW students it is replaced by Time Series and Risk Management. Note: if you follow the minor Finance and take as elective TW3560 (Voortgezette Kansrekening), you have something which is almost equivalent to the combination of both finance minors: a minor Finance XL. The minor Mathematical Finance was created specifically for others than you, as you can read elsewhere on this page.

### What will you learn

After successful completion of the minor program, the student:

- is able to explain the workings of a number of financial products and the interaction between products in financial markets;
- has some experience with the application of probabilistic and statistical methods in financial and economical problems;
- has acquired the skills to work with concepts and structures required for a rigorous foundation of (abstract) analysis and stochastics;
- has acquired knowledge and skills to manipulate and analyse, with mathematical rigor, stochastic processes and models relevant for finance.

### Course overview

The minor is composed of the following courses (for each, a short characterization is given):

**Principles of Asset Trading***WI3418TU, 6 ECTS*

Financial products are used in two ways: as an investment and as a means of attracting investors. How does this work and how can one make smart choices? What choices do companies make to finance their ventures?**Option Valuation Methods***WI3405TU, 6 ECTS*

While doing Matlab assignments you are introduced to the partial differential equation of Black and Scholes (Nobel prize 1997). You learn to price several kinds of options by computer algorithms. Insights from stochastic models are transformed into numerical methods to price and hedge products and portfolios.**Introduction to Mathematical Finance***WI3417TU, 6 ECTS*

This course is at the mathematical core of the minor. It focuses on building and analyzing models that can be applied in finance. An example is the stochastic model for stock or interest rate movement, which provides a basis to price American options.**Mathematical Structures***TW1010, 6 ECTS*

This course covers basic structures from mathematics, such as the natural numbers, induction, real numbers and completeness, functions and continuity, convergence of sequences of numbers and functions as well as series of them. All this is needed to attain the entrance level of the next course:**Probability for Finance***TW3401TU, 6 ECTS*

Mathematical finance requires a more rigorous foundation in probability than (non-mathematics) students are familiar with. This course covers probability essentials built on this foundation. Mathematical Structures and Introduction to Mathematical Finance are prerequisites. In addition to expanding your knowledge about probability, doing this course will train you in reading tersely written mathematical texts. It is a tough course, but fun!**Clinic***WI3420TU, 0 ECTS*

Weekly drop-in service hour: one of the instructors is available for questions and the department aims to have work space available. Entirely optional!

### Register for this minor

The registration for a minor takes place in two periods via OSIRIS.

**Read more**about the registration procedure.

If you want to participate in this minor you should enrol via Osiris and submit the following documents to onderwijscoordinatie-EWI@tudelft.nl no later than **April 15th**:

- A motivation letter: pdf format, 1 page, following the specifications below.
- A pdf-file (
*one*) containing an overview of your bachelor study results (TU Delft students: Study Progress overview from OSIRIS)

The motivation letter should consist of a numbered list, addressing the following four items/questions. For each, write a short and original answer of no more than 60 words.

- Why you want to enrol in this minor and not the (regular) minor Finance?
- The mathematics courses in this minor are hard---why do you think you can do it?
- What is the most interesting and/or beautiful piece of mathematics you know? Why is it interesting/beautiful?
- Anything you might want to add that may convince us this minor really is for
*you*.

What is important for you to know is that this is a demanding minor, intended for students that know why they want to do it and that are willing to do the hard work it takes to learn and practice the mathematicians’ way of thinking. The selection procedure is intended to ensure as much as we can that you have chosen it for the right reason and that you have what it takes to succeed.