Matrix calculus for finance

[NumeroUno]

Hi,

I am looking for a book that covers matrix calculus as it is used in portfolio selection and other similar problems in finance.

I recently looked over a bunch of vector calculus books from the library, and concluded that these books are probably more detailed than what I really need.

It seems that matrix calculus problems in portfolio selection are very similar to each other; there is some vector, let's say v, premultiplied by a symmetric covariance matrix and the product is then post-multiplied by the same vector v.

So if we have a covariance matrix S, and we want to find the minimum value of v' S v, it's pretty easy, right... We take the derivative with respect to v and get 2 S v, and then set this equal to 0 and solve for v.

I haven't had much difficulty with these types of problems, until recently, when I had a problem where, instead of a vector of scalar values, v, the covariance matrix was instead pre and post multiplied by a vector u, which was a function of v, and I needed to differentiate with respect to v using the chain rule. This threw me off a little bit.

Yeah, maybe I sound like a moron to most of you. I can write decent code, though. My goal is just to get through the quant classes and focus on the coding side of things, moreso than math.

Anyways, I am looking for a book that has a bunch of examples, and covers the chain rule and other simple rules for matrix calculus, as used in finance.

Is there such a book?

Thanks.

 

[Quasar Chunawala]

@NumeroUno , Dan Stefanica's book on Linear Algebra is geared towards applications of matrix theory in mathematical finance.

https://www.amazon.com/Linear-Algebra-Primer-Financial-Engineering/dp/0979757657

 

[NumeroUno]

@NumeroUno , Dan Stefanica's book on Linear Algebra is geared towards applications of matrix theory in mathematical finance.

https://www.amazon.com/Linear-Algebra-Primer-Financial-Engineering/dp/0979757657

Thanks. Does it get into calculus, though, or just algebra.

From the back of the book, it looks like it covers the minimum variance problem and the maximum expected return problem, but these are really easy. Looking for matrix calculus that is slightly beyond these problems, in terms of difficulty.

 

[Quasar Chunawala]

I haven't purchased and read the text myself. Others on the forum might be better qualified to answer that.

But, the TOC says, there is a whole chapter on efficient portfolios and Markowitz theory.

 

[NumeroUno]

I haven't purchased and read the text myself. Others on the forum might be better qualified to answer that.

But, the TOC says, there is a whole chapter on efficient portfolios and Markowitz theory.

Hi Quasar,

I really appreciate your trying to help.

I'll check it out, but I have done okay with the maths related to mean-variance optimization.

The math problem I had trouble with was slightly more complicated than mean-variance optimization. Not by much, but just by a little bit.

I may just need to bite the bullet and try to make it through a book on vector calculus, but the notation is just crazy in those books.

Thanks.

 

[Daniel Duffy]

@NumeroUno
Is this what you mean by Matrix Calculus

Matrix calculus - Wikipedia

 

[NumeroUno]

@NumeroUno
Is this what you mean by Matrix Calculus

Matrix calculus - Wikipedia

yes, exactly. this wiki page is actually a decent reference, although i wish there were a book with problems and solutions.