Since August 2022 customers have to be asked if they are interested in sustainable investment when entering a pension contract. Hence, the provider has to be prepared to offer suitable investment opportunities. Further, the provider has to manage the new risks and chances of those assets in the whole portfolio. We therefore especially look at possible consequences for optimal portfolio decisions of a life insurer and suggest modeling approaches for the evolution of the demand and the sustainability ratings for sustainable assets. We will solve various portfolio problems under sustainability constraints explicitly and suggest further research topics. As a special feature for a life insurer, we particularly look at the role of the actuarial reserve fund and the annual declaration of its return.