Date of Award


Document Type


Degree Name

Master of Arts in Mathematics



First Reader/Committee Chair

Chavez, Joseph


This paper covers mathematical methods used to conduct actuarial analysis in the short term, such as policy deductible analysis, maximum covered loss analysis, and mixtures of distributions. Assessment of a loss variable's distribution under the effect of a policy deductible, as well as one with an implemented maximum covered loss, and under both a policy deductible and maximum covered loss will also be covered. The derivation, meaning, and use of cost per loss and cost per payment will be discussed, as will those of an aggregate sum distribution, stop loss policy, and maximum likelihood estimation. For each topic, special cases based on distribution will be described and discussed. These methods and subjects are used to assess and manage risk, typically for insurance providers, but can also be adapted to a number of other fields.