Ruin theory, sometimes referred to as collective risk theory, is a branch of actuarial science

Actuarial science

Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries. Actuaries are professionals who are qualified in this field through education and experience...

 that studies an insurer's vulnerability to insolvency based on mathematical modeling of the insurer's surplus.

The theory permits the derivation and calculation of many ruin-related measures and quantities, including the probability of ultimate ruin, the distribution of an insurer's surplus immediately prior to ruin, the deficit at the time of ruin, the distribution of the first drop in surplus given that the drop occurs, etc.

It is also considered as an area of applied probability

Applied probability

Much research involving probability is done under the auspices of applied probability, the application of probability theory to other scientific and engineering domains...

 because most of the techniques and methodologies adopted in ruin theory are based on the application of stochastic processes.