ABSTRACT
This chapter and Chapter 3 are devoted to two connected topics. First, we explore the structure of the payments an insurance organization provides during a given time period. Secondly, we consider the solvency of the insurance process or, more specifically, the size of premiums sufficient for the insurance organization to meet its obligations. We begin with one insured unit. It may be an individual or an organization; we will
use the terms “client” or “insured”. In this case, our goal is to explore the probability distribution of the payment of the company to a particular insured. Next we consider the aggregate claim coming from many clients. Here, the most im-
portant problem consists in approximating the distribution of the aggregate claim in the case when the number of clients is large. “Good” approximations will allow us to estimate premiums acceptable for the insurer. Chapter 3 concerns the portfolio of risks as a whole. In this case, the objects of study are
the random number of claims coming into the insurance organization, the total payment the organization should provide, and again acceptable premiums. In both chapters, we consider only a single and sufficiently short period of time, and
all models in these chapters are static. Once we have studied how the company functions during a short period, we will proceed in Chapter 4 to insurance processes which run over extended time periods; that is, to dynamic models.
