The article defines the essence, principles, transformation of functions and elements of financial intermediation management as the central institution of economic growth in the context of spread of digital trends. While considering the evolution of the concept of the business model of banks as financial intermediaries, the authors have revealed the principles of functioning of their adaptive business model in the conditions of proliferation of digitalization processes, wherein a customer-oriented sales approach, effective innovation development, and organizational flexibility became the main principles. To implement the adaptation business model, a system of transformation measures aiming at creating the main banking product, customer service technology, non-banking services has been substantiated. It has been proved that the evolutionary progress and the processes of digitalization led to the need of banks, based on the adaptive business model, to create an ecosystem as an effective integration market strategy that provides functional openness through any interface, the ability to create innovative products, interaction at the level of clients and institutions to increase cost, strengthening financial sustainability and increasing competitiveness. Modern tendencies concerning the transformation of the essence of an insurer as a subject of financial intermediation, principles and approaches of insurance of new types of assets and risks have been systematized; reactions to the spread of digital technologies and support of digital trends in the insurance market have been revealed; the need to change the insurers business model has been justified.