Mathematical model for the analysis of environmental risk factors

Abstract

The article studies the economic consequences of harmful effects on the environment. A mathematical model has been developed for the analysis of environmental risk factors. When constructing a model, the probability of an insured event depending on time is taken into account. It is shown that different probabilistic impact models can be used for different categories of risk factors. The development of a dynamic model is based on the methods of probability theory, actuarial mathematics and, accordingly, on the, numerical methods and simulation methods. Analytical expressions for the risk factor integral value of environmental management are obtained in the work. The mathematical calculation of the distribution function, or the survival function before the time period occurrence of an insured event in different cases is performed, namely: in the case of a risk factor with a constant intensity, in the case of gradually emerging risk factors with their constant intensities, in the case when the survival function is decreasing at a linear rate, as well as in the case when equipment wear and tear leads to an exponential increase in the risk intensity.

Keywords

• environmental risk factors
• dynamic model
• survival function
• risk intensity function
• insurance payments
• insured event