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
What a load of CRAP that sharepoint isn't cut out for what the op wants to use it for. Especially the "Do not get yourself wrapped up in SharePoint" comment from ChaosPandion. Maybe he thought it to difficult and gave up...
Sure SharePoint development takes some getting used to, but it is able to what is wanted by the op most definately. SharePoint is built using ASP.NET so anything you do in ASP.NET can be used / ported to SharePoint. It is not a standalone product, but a DEVELOPMENT PLATFORM. It will scale to serve that many users, using multiple WFE's (Web Front Ends) and a SQL Cluster as backend.
The question here is: is sharepoint the most suited platform for building this site? Then I would have to answer, probably not, seeing as the wanted functionality is almost all custom development. If you plan on doing web content management as well, then yes, SharePoint is definately worth looking into. Also, SharePoint takes away all (or at least most :-D) authorisation and authentication wories. It is Department of Defense certified. And if the offered out of the box security is not enough, just write an authentication provider (seeing as SharePoint uses ASP.NET's provider model).
To answer your questions:
The bank IT told us that SharePoint has in fact lots of other features that will help us make the project more efficiently - for example, it seems that SharePoint has some built-in scalability and high availability technologies.
SharePoint is farm based, to which you can add machines, having each machine perform a different task, which means either app server, index server, WFE, document conversion services., WFE's can be behind a load balancer to distribute requests. Also I want to mention the web content management again.
I heard saying that SharePoint development is very tedious, that the platform cannot be very easily customized, etc.
Like I said, SharePoint is based on ASP.NET, so it is as much customizable as ASP.NET is. You could even create an ASP.NET web site, put all UI in Controls and then use those is SharePoint, maybe even have the controls use it's own database. As for it being tedious, not really. It's just DIFFERENT and deployment / testing is not like normal deployment / testing. SharePoint uses so called solution files (.wsp files), to package up functionality and deploy it to the server. This IMHO makes it possible to deploy functionality in a very modular way. Furthermore, there are loads of cool open source projects out there that make sharepoint development much easier and also provide cool extensions to "pimp" your site and make it more fun and easy to use for end-users.
Nuff said....