# Mathematics and Finance

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 the former and insight and skill regarding the latter are necessary to participate in this world, 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 finance 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 honest, 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 (more than you are used to) mathematics is needed. 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.

### Intended for whom?

Students from LR, WB, MT, TN, MST, TI, EE, and TW (see note below), provided they possess ample prerequisite skills and knowledge. Good knowledge of and strong skills in mathematics, enthusiasm for abstract mathematics. 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. Being able to solve three quarters of the problems from the book, and not just the computational exercises but also the insight ones, is what you should aim for.

### The programmes

**Study goals**

After successful completion of the minor Mathematical and Finance the student:

- understands 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.

The diagram below provides an overview of the minor Finance and the minor Mathematics and Finance and should help you decide which suits you best. Three of the courses are considered core finance courses and present in the programme of both minors, these are the red squares. For the minor Finance one should add the green courses, for Mathematical and Finance the blue ones. The courses are plotted with respect to two axes, the horizontal one ranging from fundamental to applied and the vertical one ranging from general to (more specific) finance. The character of each minor is now clear from the picture: Mathematics and Finance adds courses on the fundamental side, Finance on the applied side. Some courses are in fact quite general in nature, but focus on finance applications (Time Series, Monte Carlo). Here are brief course descriptions for the minor

Finance courses:

**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!

**Note for students TW**

As Mathematical Structures is part of the BSc programme Applied Mathematics, for you this course of the minor Mathematics and Finance is replaced by Times Series and Risk Management. However, the minor Mathematical Finance was created not specifically for you, for the following reason: if you do the minor Finance and choose TW3560 (Voortgezette Kansrekening) you have something which is almost equivalent to the combination of both finance minors, a minor Finance XL.

**Selection procedure**If you want to participate in this minor you should enrol via Osiris

*and*submit the following to

*onderwijscoordinatie-EWI@tudelft.nl*no later than May 31st:

- A motivation letter: pdf format, 1 page, according to 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?
- 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 (which almost surely is different from what you are used to). 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.

### Admission

### More information

**Dr.ir. L.E. Meester **Faculty Electrical Engineering, Mathematics and Computer Science

Applied Probability

+31 (0)15 27 87258

L.E.Meester@tudelft.nl

### Testimonial

The courses offered in the minor ‘Mathematics and Finance’ are quite diverse, since it covers two different ‘worlds’ (theoretical and practical).

Read more about the story of Bart, student Mechanical Engineering.