AGGREGATE RISK MODELS: RISK MEASUREMENTS, RISK ALLOCATION METHODS, AND THEIR APPLICATION TO COMBINATION REINSURANCE - Maziyah Wildan M, Lailatul
The aggregate model of two random variables can be viewed as a reinsurance model. The reinsurance model can also be said to be a risk allocation method, namely dividing insurance and reinsurance risks. The Stop-Loss model is used by Zhou dkk. (2011) by adding budget constraint to the total loss covered by insurance. Furthermore, Liu & Fang (2017) uses the optimal Quota-Share model based on the perspective of insurance and reinsurance by minimizing total insurance and reinsurance expenditures. Meanwhile, Putri dkk. (2021) uses a combined reinsurance model by integrating Quota-Share and Stop-Loss reinsurance while minimizing the value of text. The optimal reinsurance model has been in great demand among researchers with a variety of approaches. Fang dkk. (2018) discusses optimal reinsurance by paying attention to premium calculations. Meanwhile, Syuhada dkk. (2021) uses a reinsurance combination model by minimizing the Expected Shortfall (ES) value of total insurance and reinsurance loss expenditures to obtain an optimal model. The ES risk measure expresses the mean of all losses that exceed their tolerance limits at a certain period and a certain confidence level. The tolerance limit in question is the Value-at-Risk (VaR) value. According to Klugman dkk. (2019), ES risk measures are more coherent than other risk measures such as VaR. Therefore, this thesis will determine the reinsurance model based on the ES risk measure, with the loss of the reinsurance being modeled using the Shanker distribution due to its flexibility.