COPULAS AND EVALUATION OF RISK MEASUREMENT AND -BASED CAPITAL ALLOCATION IN A CONTEXT OF TAIL DEPENDENCY

In this paper, we construct an extension of Spearman’s copula and evaluate the risk measure TVaR (Tail Value at Risk) and the TVaR-based capital allocation for an insurance portfolio whose risks maintain a tail-dependency relationship via this new copula. Assuming that the portfolio comprises two lines of business whose risks are identically distributed according to the exponential law and then according to the Pareto law, we derive an explicit formula for the risk measure TVaR and the explicit formula for the capital to be allocated to each line of business in the portfolio to ensure the solvency of the insurance company.