Should I use MATLAB or GAUSS for statistical analysis?

Have you ruled out http://www.r-project.org/ already? It's an open source freeware workalike for S. There's a lot of stuff for it canned, and it can churn big matrices around. I dunno what you'd need it to do, and likely wouldn't be able to make sense of any reply (financial probably means time series, which means me running away in panic leaving Xeny-shaped holes in the walls), but it can do a damn lot. Did I mention it's free?

Well, galvatron did, anyway. I've used R for some simple monte-carlo simulations and hierarchical linear models, and it's worked fine, no complaints. The guy across the hall uses it for event-count time-series models and lauds it on a weekly basis.

I have done work in Gauss, but not MATLAB. I know that Gauss is fairly expensive (~$1200). I used it for maximum likelihood estimation. I would look into what system has the most suitable packages for your particular application. (I have also heard that all the cool kids use R, so check into that too.)

Please see my previous http://metatalk.metafilter.com/mefi/4030#96759. Matlab is expensive, but you have to contact them for a (academic / student ) quote.

Also, you can download a student version of S-plus (with which I tinker) if you (or someone you know) has a .edu address.

I'm sure you've googled, but http://www.google.com/search?hl=en&lr=lang_en&ie=UTF-8&oe=UTF-8&q=r+matlab+gauss+modeling+smay help, too.

Also, you can download a student version of S-plus R and S-plus should be pretty interchangeable, with the exception that you won't get push-button stuff with R.