Is the client or vendor responsible for writing the BRD?
I am a BA in a company that provides insurance solutions to clients.
We work in a hybrid methodology between waterfall and agile (project divided into Sprints, each Sprint will go as a waterfall life cycle).
Now I know that the solution Specification document should be prepared by myself, but I'm not sure about the BRD.
Whose responsibility is writing a business requirements document (BRD)? Should it be from the client side or vendor side?
The team as a whole (developers and client) should take responsibility for creating any documentation. It's a collaborative effort and to maximise productivity the team should try to avoid having unnecessary hand-overs of documentation between different sub-teams.
If your sprints have a "waterfall lifecycle" then they are not sprints. Agility is not essentially about doing work in iterations but has more to do with working collaboratively to solve problems, responding to business needs and minimising bureaucracy and hierarchy. The fact that you are asking this question suggests that you are open to some alternatives, so maybe you can raise your question with the rest of the team before deciding how to proceed.