Risk theory connotes the study usually by actuaries and insurers of the financial impact on a carrier of a portfolio of insurance policies. For example, if the carrier has 100 policies that insures against a total loss of $1000, and if each policy's chance of loss is independent and has a probability of loss of p then the loss can be described by a binomial variable. With a large enough portfolio however, we can use the Poisson function

Poisson distribution

In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since...

for the frequency of loss variable where λ is used as the mean equal to the number of policies multiplied by p.