Since I've never looked into COBOL seriously I'd like to have some examples of that large class of problems C++ and VB can't handle, it sounds interesting (no irony here).

Actually, is's fairly dull. COBOL is designed for business use (that's what the B in the acronym is from) and it excels at doing business and financial tasks. COBOL has good facilities for handling money. It doesn't, for example, make the horrible error of trying to do financial calculations with floating point numbers. (Important safety tip: Don't try to do decimal math with a representation that can't handle base-10 fractions)

Regardless of this point: bear in mind that many businesses simply don't have COBOL around anymore, so yes, you'll be going for a niche. Personally I consider that to be a bad start of a career.

All computer languages target a niche. You are, however, badly misjudging the amount of COBOL in use as well as the amount being written brand new. There's an enourmous amount in every major (and most minor) financial institutions, as well as most places that have major financial departments. (Which includes the AP, AR, and payroll departments) It's also in a lot of other places you might not expect.

It wouldn't, quite bluntly, surprise me to find that there's more new COBOL code being written than C++ code. By a factor of two or more. (Probably more) There's certainly an order of magnitude or four more COBOL in use than C++.