GENERALIZED GAMMA DISTRIBUTION: MODEL EXPLORATION AND RISK MEASURE - Prasetyani, Etika
Generalized Gamma Model is generalization of Gamma model which has three non-negative parameters, i.e a; d; and p. Parameter a is scale parameter, while parameter d and p are shape parameters. Generalized Gamma Model is a good model candidate which used in risk measurement. This model can construct some models which accomodate skewness and it can be used in risk data. In insurance and finance, risk often comes from several individual risks which are referred as aggregate risk. Therefore, it is needed to construct aggre- gate model. In spesific, the construction of the aggregate model is constructed from single risk distribution of Generalized Gamma. Risks in aggregate model can be independent or dependent. The dependence will affect to probability function and distribution function of aggregate model. Risk can be measured through risk measure. Value-at-Risk (VaR) is the most popular risk measure to predict losses. In calculating VaR, the exact form of the probability fun- ction or distribution function is needed. Meanwhile, probability function and distribution function of Generalized Gamma aggregate model are difficult to obtain directly, thus Translated Gamma Approximation is used. Hence, the calculation of VaR for Generalized Gamma aggregate model will be calculated numerically and also using concept of lower bound for aggregate.