Interplay of Insurance and Financial Risks with Bivariate Regular Variation

It is known that for an insurer who invests in the financial market, the financial investments may affect its solvency as severely as do insurance claims. This conclusion is usually reached under an assumption of independence or asymptotic independence between insurance risk and financial risk. Such an assumption seems reasonable if the insurer focuses on the traditional insurance business that does not interact much with the capital market. However, we shall argue that at least for insurers who participate in financial guarantee insurance and as a result cause systemic risk, asymptotic dependence between insurance and financial risks needs to be considered. Under a bivariate regular variation structure, we investigate the interplay of insurance and financial risks, and show that the asymptotic dependence introduces extra risk for the insurer’s solvency.