I use SMS Backup + [1] which saves all my text messages to my Google account allowing me to easily search and archive. It's followed me through android phones for many years, automagically installing as I sign-in for the first time on each 'new' device.
They are likely to be either Bloomberg messages or on banks' internal chat systems, similar to IRC but recorded. For example Mindalign is a chat system that was spun out of UBS and bought by Microsoft.
