Diffusion approximations in collective risk theory

Collective risk theory is concerned with the random fluctations of the total assets, the risk reserve , of an insurance company. Consider a company which only writes ordinary insurance policies such as accident, disability, fire, health, and whole life. The policyholders pay premiums regularly and at certain random times make claims to the company. A policyholder's premium, the gross risk premium , is a positive amount composed of two components. The net risk premium is the component calculated to cover the payments of claims on the average, while the security risk premium , or safety loading , is the component which protects the company from large deviations of claims from the average and also allows an accumulation of capital. When a claim occurs the company pays the policyholder a positive amount called the positive risk sum .