Everyone has to deal with matters of insurance and financial risk at various times in life. Premiums are paid for either complete or partial insurance coverage against risk. Financial risk refers to the money a company or other entity can lose, including underpaid profits, and is modeled in a number of ways. Gamma distribution and the general gamma family are among the most popular models for modeling financial data. This study seeks to assess and determine the effectiveness of the extended gamma distribution family in measuring risk using a single number in the form of a risk measure. Further, this study seeks to understand the functional of distribution on the positive semi-axis, satisfying (some of) the desirable properties. A list of the most popular risk measures is provided as well as the different premium principles, the VaR and the optional TVaR, as well as the desirable properties of risk measures, including but not limited to non-negative loading, sub-additivity, consistency, scale invariance, no rip-off and objectivity.