Book recommendation for masters student with no maths background

Question

I have been accepted for a masters course in computational finance that is largely mathematical, and is most suited for students who have studied either mathematics or physics in their bachelor's degree. I however, have done business/finance. I believe the reason why I have been offered a place is because I studied lots of maths in my free time (I really regret not doing maths as my degree, and I am trying to compensate for that by doing it on my own). I would solve STEP questions whenever I had free time off work. I am already week 5 into my course and it has been OK so far. But stochastic processes starts to become a bit too much for me (and it is a core module).

To give you an idea of what I have done so far: for our quantitative module, we derived kolmogorov equation, used similarity methods to solve it; we defined brownian motion; we then learned quickly about stochastic processes; Ito's lemmas and most recently we have derived the Black-Scholes equation. Lecturer mentioned about parabolic and hyperbolic PDEs (I know what a PDE is, but not heard about those classifications).

For linear algebra, I think I am coping, but if you have a nice quick intro book for that, would be awesome; we have "done" (rushed through) SVD and PCA so far (no examples were provided). Even though I understand the concepts of both, I really need to do a few examples (not sure whether they can be manual for PCA?).

And finally, stochastic processes for finance. This is really a disaster. But this is mostly because of the lecturing style than anything else. I have learned chapters 2 to 7 inclusive of Ross's "First Course in Probability". Thus, I have learned about the marginal density functions, convolution etc. To be honest, so far it was basic probability. The last lecture however, started going into Fourier transforms, and I lost the plot at that point.

I am certain it is doable to pass the course, but I want more, I want a somewhat better understanding of what is going on. I study every day from very early until very late, so I hope I can at least partially catch up with other students. Not sure whether this question is appropriate here, and whoever is still reading, I appreciate it. If you have any book recommendations that really are useful for my purposes, please let me know.

Answer 1

I recommend checking out the recent book An Introduction to Stochastic Differential Equations by Evans, who is the author of a very popular PDEs textbook. An Introduction to Stochastic Differential Equations is a short, intuitive, friendly book. Here's the amazon description:

This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive "white noise" and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Itô stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).

For linear algebra, I recommend Gilbert Strang's book Linear Algebra and its Applications, which makes the subject seem easy and provides good intuition.

Answer 2

I recommend An Elementary Introduction to Mathematical Finance by Sheldon M. Ross.

From the Amazon review:

This textbook on the basics of option pricing is accessible to readers with limited mathematical training. It is for both professional traders and undergraduates studying the basics of finance. Assuming no prior knowledge of probability, Sheldon M. Ross offers clear, simple explanations of arbitrage, the Black-Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model. Among the many new features of this third edition are new chapters on Brownian motion and geometric Brownian motion, stochastic order relations, and stochastic dynamic programming, along with expanded sets of exercises and references for all the chapters.

For partial differential equations, I recommend The mathematics of financial derivatives: a student introduction by P. Wilmott, S. Howison, and J. Dewynne.

This book avoids almost all discussion of diffusion processes associated with option pricing, focusing instead as much as possible on the associated PDE’s. Relatively easy to read; it goes much further on numerical approximation schemes, American options, and some other PDE-related topics.

For linear algebra, I can suggest Schaum's Outline of Linear Algebra.

Answer 3

Hi I am currently a Mathematics Masters student having come in from a course with only moderate mathematical content. I use Walter Rudin's 'Principles of Mathematical Analysis' as my first stop to check anything related to analysis .i.e. Fourier Transform. It may not be the best choice of book for linear algebra etc but I thought I would share and recommend having a look!

Answer 4

I recommend those books

Satish Shirali,_Harkrishan Lal Vasudeva. "Multivariable Analysis",
Derek J. S. Robinson "A COURSE IN LINEAR ALGEBRA WITH APPLICATIONS (2nd Edition), 
ROBERT B. ASH, MELVIN F. GARDNER, "Topics in Stochastic Processes"

may be are usefull,