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- 2/18/16
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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.
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.
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