Introduction. A mathematical model is presented for assigning protection objects to certain risk categories in the field of fire safety. The model is based on the concepts of the probability of adverse effects of fires causing harm (damage) of various extent and severity to the life or health of citizens, and the acceptable risk of harm (damage) from fires. Goals and objectives. The purpose of the study is to develop the procedure for assigning protection objects to a certain category of risk of harm (damage) based on estimates of the probability of fires with the corresponding severity consequences, to determine the acceptable level of risk of harm (damage) due to the fires, to calculate and develop numerical values of criteria for assigning objects of protection to the appropriate risk categories. Methods. The boundaries of the intervals corresponding to certain risk categories are determined by dividing the logarithmic scale of severity of adverse effects of fires into equal segments. Classification methods are used to assign objects of protection to a specific risk category. Results and discussion. Based on the level of severity of potential negative consequences of a fire, risk categories were determined for groups of protection objects that are homogeneous by type of economic activity and by functional fire hazard classes. The risk category for each individual object of protection is proposed to be determined using the so-called index of "identification of a controlled person" within a group of objects that are homogeneous by type of economic activity and class of functional fire hazard. Depending on the risk category, the periodicity of planned control and supervision measures in relation to the specific object of protection under consideration is determined, taking into account its socio-economic characteristics and the state of compliance with fire safety requirements by the controlled person. Conclusions. To develop criteria for classifying protection objects that are homogeneous in terms of economic activity and functional fire hazard classes, the probability of negative consequences of fires, that are causing harm (damage) of various extent and severity to the life or health of citizens, and the acceptable risk of causing harm (damage) as a result of fires, is used. The risk category for each individual object of protection is determined taking into account socio-economic characteristics of the object that affect the level of ensuring its fire safety, as well as the criteriaof integrity of the subordinate person that characterize the probability of non-compliance with mandatory fire safety requirements at the object of protection. Calculations are made and numerical values of criteria for assigning protection objects that are homogeneous in terms of economic activity and functional fire hazard classes to a certain category of risk are proposed. Key words: object of protection, probability of fire, acceptable level of risk, risk category, dangerous factor of fire, death and injury of people.
Formalization of the “risk” category during the realization of reinsurance operations on the basis of the economic and mathematical apparatus