This is my first "soft question" so I hope it is alright.
I graduated from a well-respected institution a few years back with an undergraduate degree in Finance and Economics. From there I spent about 6 years in the finance "industry" and actually had a very research-intensive job, well-beyond what you might typically associate with asset management.
In 2009 I applied to a handful of Finance PhD programs and got 2 interviews, but ultimately no offers. After much self-reflection I think the main deficiency in my profile was a lack of rigorous math and stats preparation. Although I had a 4.0 and graduated #1 in my class, I had only taken Calc 1 and 2, 1 stats class, etc.
My question is, now that I have been working tirelessly on remedying these shortcomings, how can I further improve my knowledge base. Keeping in mind that I dont want to "mis-learn" things before beginning, what courses and self-studying options should I pursue. If it is of any value, my research interests are in theoretical asset pricing.
So far, in the last 2 years I have taken the following steps:
-Finished Calc 3 -Finished Linear Algebra (undergrad-level) -Taken 6 grad-level courses in statistics (en route to MSc) -Begun a 1 on 1 study of probability and measure theory with a grad professor -Enrolled in graduate-level linear algebra
I am asking this question because I can't think of a more helpful and insightful group of mathematicians, and on the off-chance that others who are considering careers in Finance (academic or industry), can learn about the necessities for rigorous mathematics to achieve these goals.
Any answer is welcome, but specific texts and/or courses to seek out would be most helpful to me.
For example, I am taking the LA course to help with my ability to understand linear transformations and higher-dimensional models that will be necessary in econometrics and other courses.
Also, while I never had a course in Analysis, I worked through a few books to try and get the foundation so that I could study PhD-level measure theory. Prior to starting this course, I worked through the Springer Undergraduate Text called "Measure, Integral, and Probability," and found it a perfect bridge to Resnick's "A Probability Path."
The most logical explanation to continue these studies seems to move on to a beginning course in Stochastic Processes/Markov Theory. With this example specifically, am I missing any foundational coursework that is vital/will not be developed in the text? What texts would the community recommend for this subject?
I hope this question is of value for others who may be in similar situations. Any specific guidance is welcome.