Typically, devices are banned from restricted areas (trading floors). Where BYOD is "allowed", apply a corporate profile which prevents the installation of problematic apps. What these people do outside of office hours can get them in trouble too.

NYSE Rule 36 seems to cover this:

https://nyseguide.srorules.com/rules/document?treeNodeId=csh...

(d) Floor brokers must maintain records of the use of telephones and all other approved alternative communication devices, including logs of calls placed, for a period of not less than three years, the first two years in an accessible place. The Exchange reserves the right to periodically inspect such records pursuant to Rule 8210.

UK rules seem to ban BYOD?

https://www.lawyer-monthly.com/2018/03/fca-says-employees-ca...