RISK MEASURE OF DEPENDENT TAIL VALUE-AT-RISK FOR AGGREGATE RISK MODEL AND ITS APPLICATION - Parulian Josaphat, Bony
In actuarial science, the aggregate risk model plays an important role. In general, the aggregate risk model can be viewed as a collective risk model where the claim severities and the number of claims are not always independent of each other. This means that the individual risk model is a specification of the collective risk model when the number of claims is given. Aggregate risk can be quantified into a certain number by using a risk measure. One widely known risk measure is Tail Valueat- Risk (TVaR). TVaR is the average of the values of random risk that exceed the Value-at-Risk (VaR). The classic risk measure of TVaR does not take into account the excess of another random risk (associated risk) that may have an effect on aggregate risk (target risk). One of the objectives of this study is to calculate the risk measure of aggregate risk by taking into account another risk that involves Copula. This risk measure is called Dependent Tail Value-at-Risk (DTVaR). DTVaR is a coherent and law-invariant convex risk measure. Similar to TVaR, DTVaR also calculates the mean loss of risk on the tail. The second to fourth central moments in the tail of the distribution around the DTVaR also need to be calculated to obtain a new risk measure involving variability, skewness, and kurtosis called Copula-based Conditional Tail Central Moment (CTCM). One specification of CTCM is the Dependent Conditional Tail Variance (DCTV). The risk measure of DTVaR can be optimized by using DCTV as a component of the constraint function. Furthermore, DTVaR is applied to predict the mean loss in energy risks.