Is it ok to install a SSAS 2016 instance next to a SQL Server 2014 instance? Should I expect any problems installing a SQL Server Analysis Services 2016 tabular instance next to a SQL Server 2014 database engine? (e.g. due to an update of some shared components)

I'm mostly worried about any issues related to the running database engine.

Thanks.
It is best to keep a server dedicated to a single version of SQL Server and/or its components. You can run into connectivity issues or have components stop working as expected due to the mismatched version of the shared components. I recently had an instance where someone upgraded the SSIS components and prevented us from opening packages properly on that box any more. 

Additionally, if you can avoid it, keep SSAS and the engine separated as both do not like to share resources properly. You could end up with performance issues if you do not configure things properly.