Digital technologies foster intensification of transformation processes on insurance market. Insurance market development depends on efficient introduction of digital insurance technologies, which give an opportunity to compete with global innovation technologies providing information security on global space. The article studies acute issues of insurance market development in conditions of digital technologies. On the basis of digital insurance analysis the article shows importance of further introduction of digital technologies into insurance industry in order to raise quality of insured’ protection and to develop insurance business in digital economy. The authors came to the conclusion that digital insurance is a result of the stable and effective development of finance market. Factors influencing insurance market development were identified, the impact of COVID-19 epidemic on insurance industry was demonstrated and acute types of insurance in these conditions were studied. The role of finance theory and insurance education in insurance market transformation was described as well as the necessity of system upgrading of education technologies.