Abstract
This article deals with the problems of constructing and analyzing a collective risk model for an insur-ance company when the time evolution is defined on a general time scale. The relevance of the study isdetermined by the need to describe pvremium accumulation and claim payments occurring at discrete orirregular time instants within a unified analytical framework. The characteristic features of the classicalrisk model and its extension to time scales are analyzed, and the need to investigate the behavior of theprobability of non-ruin under such generalization is identified and justified. On the basis of the study, theauthors construct an analogue of the classical model on time scales and derive a dynamic equation for thedistribution of the number of claims. An integral equation on a time scale for the probability of non-ruinis formulated. Conditions ensuring the correctness of the constructed model are established. It is provedthat the probability of non-ruin defined on a family of time scales converges pointwise to the correspondingprobability in the classical continuous-time risk model as the graininess function tends to zero. It is shownthat the proposed approach provides a rigorous justification of the transition from discrete to continuousrisk models.