Definitely have a lawyer look it over because when you leave this firm they really try to block you from doing any job in the similar space.
+1 to the lawyer. Yes, it's expensive just like any other professional, but the potential downside if you make a mistake doing it yourself is catastrophic. Think of it as insurance.
Paying for legal advice at this point is a waste of money unless you are willing and able to take on the great expense and hassle if the company decides to come after you at a later date. It's very easy for a lawyer to give you an initial opinion, but quite a different story if you are later challenged by a company with deep pockets. Being "right" won't pay your bills. Better to disclose your plans/concerns to the employer right now, then decide your direction based on their response. Otherwise you'll be working for them under a cloud of concern, and that's never a good position to be in.
The text you quoted doesn't seem to give your employer any rights to work you do for yourself on your own time, unless you choose to include such work in the work you do for them (which is prohibited by first paragraph of the contract you quoted.) However, if you have a great idea during your work day about how to solve some problem in financial analysis, then you wouldn't be able legitimately use it for your own work, which would suck. And if you had the idea on your own time and used it for your own work, then your employer might later wonder whether you actually came up with the idea while they were paying you. There's definitely some potential for conflict of interest here. If I were the employer I would probably not feel comfortable hiring someone who was working on their own competing product or service, and if I found out they were working on such a project in secret without discussing it with me first, it would seem like a breach of trust. I second what DeeDeeTwo said about being careful with lawyers. There are a lot of shysters out there who will drain you dry if you let them. I've seen a multi-million dollar business picked clean over a period of years once lawyers were brought in to help 'resolve' some disputes.
It would appear that since you are quoted as being "contractor" in the agreement you refer to, that indeed you are not formally an "employee". Are you being paid on a 1099 ? If so, you should formally add a section to the agreement that you incorporate "Prior Art" into your work activities. As such, the Company may not have legal rights to certain intellectual properties that you have independently established before your work for them begins. I am assuming by the wording in your original post that you are not being offered a formal position as a full-fledged W-2 employee of the Company. Please elaborate. Before I began a stint at a hedge fund, I included a "prior art" addendum into my employment contract and it stood. I also listed in general terms what such prior art included. "Intraday Automated Trading Algorithms", for example, is a general term. If you are 1099 - IMO, sounds like they want their cake and eat it too. Contractors are generally employed based upon their established skills.