Introduction. Employees of Emercom of Russia often participate in extreme tourism during their vacations, which helps to maintain their professional physical fitness. They are also attracted to help tourist groups that find themselves in a difficult situation in nature in a particular destination. Participation in extreme tourism is associated with the risk of injury. A general approach to the assessment of the impact of the management of the safety of tourist services in the instances associated with extreme tourism on insurance risks is presented. The purpose of the article is to create models for assessing the risks of extreme recreation. To do this, it is necessary to analyze the routes of extreme recreation in destinations from a mathematical point of view, and, based on this, to propose a number of management measures related, among other things, to insurance. Research methods are based on the use of the theory of discrete mathematics in the construction of a weighted graph describing the risks on the routes of tourists. The model allows us to quantify the risks on individual routes and, therefore, to build a target criterion for supporting the management of the safety of services in extreme tourism in a particular destination. Results and discussion. Building a graph of the route of a tourist group allows you to identify the least dangerous routes of tourist groups. This approach allows insurance companies to solve the problem of calculating the optimal and adequate amount of payments in the event of an insured event, as well as to reduce uncertainty in the actions of rescue units of Emercom of Russia. Conclusions. The methods of managing the safety of providing tourist services presented in the article reduce the probability of an insured event. Key words: insurance risk assessment, management of tourist services, tourist safety, security methods.
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