We are witnessing the emergence of the "first generation" of AI and AI-adjacent soft and hard laws such as the EU AI Act or South Korea's Basic Act on AI. In parallel, existing industry regulations, such as GDPR, MIFID II or SM&CR, are being "retrofitted" and reinterpreted from the perspective of AI. In this paper we identify and analyze ten novel, "second generation" themes which are likely to become regulatory considerations in the near future: non-personal data, managerial accountability, robo-advisory, generative AI, privacy enhancing techniques (PETs), profiling, emergent behaviours, smart contracts, ESG and algorithm management. The themes have been identified on the basis of ongoing developments in AI, existing regulations and industry discussions. Prior to making any new regulatory recommendations we explore whether novel issues can be solved by existing regulations. The contribution of this paper is a comprehensive picture of emerging regulatory considerations for AI in investment management, as well as broader financial services, and the ways they might be addressed by regulations - future or existing ones.