We need to develop quite a powerful web application for an investment bank. The bank IT would like us to build it on top of the SharePoint platform
Do you need document management? Do you need version management? Do you need to create "sites"? Do you need audience filtering? Do you need ECM (fancy word for CMS), Do you need collaboration stuff on your site? If your answer is no then SharePoint is not for you.
You said "We have never made any SharePoint programming" and for that reason alone I think you should not use SharePoint. You also say that your app is going to be "non-standard" and complex, another reason not to use SharePoint.
Sounds like you know ASP.NET so I would advice to stick with ASP.NET or ASP.NET MVC.
Hope this helps