basics for a dummie

[JJaz]

Hello to everybody,I've just started university and I'm completely new to the world of quants. Because my course in Economics offers the most interesting exams (derivatives,quantitative finance etc.) during the 4th and 5th year and I really want to start RIGHT NOW with quantitative finance,I'd like to know from you the very basics (and the books) on which building my quant-career as an autodidact.

Thank you in advance my friends,
JJaz

 

[Andy Nguyen]

Hello and welcome to Quantnet
Start here quantnet.com/guide

 

[JJaz]

Hello Andy ,thank you for the immediate answer,I've read the list of the books,can you tell me what is the mathematical and statistical background they suppose you have before you start reading?

 

[DavidH]

Hello to everybody,I've just started university and I'm completely new to the world of quants. Because my course in Economics offers the most interesting exams (derivatives,quantitative finance etc.) during the 4th and 5th year and I really want to start RIGHT NOW with quantitative finance,I'd like to know from you the very basics (and the books) on which building my quant-career as an autodidact.

Thank you in advance my friends,
JJaz

If you just started university I would suggest taking a look at several different MFE sites and look at their admission course requirements as this will give you a good idea as to what classes you should be taking and focusing on throughout your undergraduate studies. To sum up most of their requirements, you should focus on Finance, Programming (C++) and Math (at least 3-4 semester calculus, 1-2 semesters linear algebra, 1-2 semester probability).

 

[Noel]

DavidH,

What level of probability would be enough for say, MFE at Columbia? Would reading a book like Ross's "A First Course in Probability" be enough to understand and excel at the program? Or do you need to know measure theory probability, like Ash's "Probability and Measure Theory" or Billingsley's "Probability and Measure"?

My math background is that of an engineer (CalcI,II,III), Numerical Analysis, Ordinary Diff. Equations, Linear Algebra. I did not take a probability class and I would like to study the topic by myself. Now, I understand that measure theory probability requires more effort, as I would have to study Real Analysis first to gain understanding of measure theory. And then read Ash's or Billingsley's book. Whereas Ross's book I can read now, since I think the only prerequisite for it is the normal Calculus course.

I am interested in the programs at Columbia University, Carnegie Mellon and Berkeley. From what I have read, it seems like Berkeley and CMU are more math intensive than Columbia. I might be wrong. Let me know if Ross's book is enough for all 3 programs or not. If I apply to the program and get accepted, I want to be ready in order to have an smoother year.

 

[bigbadwolf]

DavidH,

Or do you need to know measure theory probability, like Ash's "Probability and Measure Theory" or Billingsley's "Probability and Measure"?

... Now, I understand that measure theory probability requires more effort, as I would have to study Real Analysis first to gain understanding of measure theory. And then read Ash's or Billingsley's book. Whereas Ross's book I can read now, since I think the only prerequisite for it is the normal Calculus course.

Ash's book is self-contained with regard to measure theory. It's one of the best texts on measure-theoretic probability out there, written with great care and meticulous attention to detail. If you work through the book conscientiously you'll have a better grasp of rigorous probability than most quants. There are other fine texts on measure-theoretic probability that also cover the necessary measure theory. Sean Dineen's book -- Probability Theory in Finance -- is another carefully written book. I look for attention to little things -- for instance, the proof that the sum of two random variables is also a random variable. Many books (Jacod and Protter, Rosenthal) give short shrift to such a fundamental result, leaving one scratching one's head about what a rigorous proof would look like.

A prior course in real analysis is not necessary but is recommended for two reasons: 1) Exposure to various convergence results (pointwise, uniform) that show what properties carry over to the limit, and 2) Enhanced 'mathematical maturity', which means understanding the need for careful arguments, understanding the importance of counterexamples, and understanding the structure of definitions, lemmas and theorems. It's possible to bypass this sequential order (for example, I learnt general topology before I took a course in real analysis)

 

[Noel]

Thanks for the reply bigbadwolf. I have a couple of follow up questions:

1) I still don't know if going to an MFE in Columbia with only Ross's type of probability knowledge will be proper preparation. From what you said, if I study Ash's I will be better prepared than most. But it seems some people do without it. I'm not trying to take the easy route, it is just that studying Ash's will take me more time. I'll have to enter into a Real Analysis class first and then tackle Ash. I don't think I have the necessary mathematical maturity to tackle Ash's book.

2) If your answer to question one is that I need to understand measure probability (Ash's book) to be able to excel at the MFE in Columbia, for example, what book would you recommend to learn Real Analysis from. I actually own the book "Mathematical Analysis" by Tom Apostol. Is this a good source? If so, which of the following chapters I need to study to get the necessary knowledge to read Ash's book?

1. The Real and Complex Number Systems.
2. Some Basic Notions of Set Theory.
3. Elements of Point Set Topology.
4. Limits and Continuity.
5. Derivatives.
6. Functions of Bounded Variation and Rectifiable Curves.
7. The Riemann-Stieltjes Integral.
8. Infinite Series and Infinite Products.
9. Sequences of Functions.
10. The Lebesgue Integral.
11. Fourier Series and Fourier Integrals.
12. Multivariable Differential Calculus.
13. Implicit Functions and Extremum Problems.
14. Multiple Riemann Integrals.
15. Multiple Lebesgue Integrals.
16. Cauchy's Theorem and the Residue Calculus.

 

[bigbadwolf]

1) I still don't know if going to an MFE in Columbia with only Ross's type of probability knowledge will be proper preparation. From what you said, if I study Ash's I will be better prepared than most. But it seems some people do without it. I'm not trying to take the easy route, it is just that studying Ash's will take me more time. I'll have to enter into a Real Analysis class first and then tackle Ash. I don't think I have the necessary mathematical maturity to tackle Ash's book.

Instead of Ash, try Capinski and Zastawniak's Probability through Problems, maybe followed by Capinski and Kopp's Measure, Integral and Probability. Just the first will give you a head start by introducing you to sigma algebras and random variables (rigorously).

2) If your answer to question one is that I need to understand measure probability (Ash's book) to be able to excel at the MFE in Columbia, for example, what book would you recommend to learn Real Analysis from. I actually own the book "Mathematical Analysis" by Tom Apostol. Is this a good source?

Apostol is even more difficult than baby Rudin and he uses general topology right from the outset to handle multivariable differentiation and integration -- something you don't need. Instead try Howie's Real Analysis or Dangello and Seyfried's Introductory Real Analysis. They both cover the absolute essentials for a single variable right up to convergence tests for power series.