This book focuses on the problems of embedding emerging risks in network flow structures. The authors' quantitative definition of risk is accepted: it is considered as a product of the resource to be treated on individual sections of the network and the probability of an adverse event on the same section of the network. The mathematical structure of network flows has long occupied a stable place in the study of operations and in the relevant sections of discrete mathematics. It finds significant application in economics, transport, industry, agriculture, military affairs, as well as in many areas of public practice. Nowadays, the risk-taking models discussed in the book would be useful in solving economic, investment, transport, logistics and other problems.