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A Model for the Insurance & Reinsurance of a Mega – Catastrophic Risk

This paper concentrates on mega–catastrophic risks whose coverage can be gained only by resorting to funds from outside the insurance industry. We propose a definition of catastrophe, mega-catastrophe, mega-catastrophic risk and insured mega-catastrophic risk. Furthermore, under suitable assumptions, we propose and analyze the decomposition of a mega–catastrophic risk in a part retained by the insurance market (using a catastrophe excess of loss reinsurance contract) and in a part transferred to the financial market (by issuing catastrophe bonds). Accordingly, taking into account the solvency constraint for the insurance business and the no–arbitrage condition for the financial market, we compute the safety loading necessary for the insurance of the mega–catastrophic risk, analyzing some of the different possible choices corresponding to different risky insurance portfolios.