Good observation, I saw the same on Wikipedia, then tried to find more information on their trading and couldn't find any. Thought it was kind of strange they'd be taking on risk like that. I think my modified list is more accurate.
Pretty much most big banks, hedge funds, international companies, big insurance companies and prime fx brokers from every part of the world. I have seen many big banks from Turkey, Middle East, Japan, China, India, Eygpt, etc... are trading against each other. Of course, there are these big traders like Goldman Sachs, Credit Suisse. Traders pretty much hate each other's gut. Given them a chance, they would not hesitate to destroy others for their own survival.
Kevin Rodgers's book 'Why Aren't They Shouting?' is indirectly quite good on this. It's more of a wander through how fx trading changed since the 1990s, in particular via technology (he became head of FX at Deutsche Bank). As others have said the list above are all brokers with very little directional betting.
Any indications of how much trading by e.g. his bank, Deutsche, is at their discretion? i.e. how much of their capital deployed is in trades DB select and how much as directed by their clients?
From memory not discussed much. It sounded as if it was just about all they could manage to keep up with the pace of technological change. And the technological direction was all about the market becoming more and more concentrated among a few big plays and the never ending compression of spreads. I remember he does mention them getting picked off by fast hedge funds and it being a constant battle to avoid adverse selection.
Seem to remember a famous academic(?) paper a good few years ago which examined Citibank's fx trading. It found that they made 100+X% of their profit from the spread, ie they lost on aggregate on positioning decisions they made.
Dunno! I may well misremember and I can't find a reference to it now sadly... This paper is pretty good on the OP topic. It's a bit dated but maybe as it's pre-crash but most should find it informative. Just read section 2: https://pdfs.semanticscholar.org/c80f/838f41fb428426c5f06a29c34def76d4992b.pdf