Zero knowledge proof of fund

Is there a way to prove to someone that I own a certain amount of ETH without disclosing any other information? (obviously not the address but also not the real amount of ETH I have)

A way this could work:

1. Prove ownership of an address by signing something
2. Provide some custom identifier that identify you (first and last names for instance). The system should ensure no proof was ever generated for the same address with a different identifier. This will be included in the generated proof but should be hidden from blockchain inspection.
3. Provide who the proof is to be generated for ("HSBC Bank"). This will be included in the generated proof (also hidden from blockchain inspection) as well as the current timestamp

2 ensures you cannot reuse a proof from someone else, and 3 shows to the counterparty the proof was generated for them