A Risk-Theory Model to Assess the Capital Requirement for Mortality and Longevity Risk (Restricted Version)

There is considerable uncertainty regarding the future development of life expectancy that leads to significant change in many fields of insurance market. Pricing annuity products and mortality-linked securities seem primary goals of actuarial literature. At the same time, the valuation of non-hedgeable liabilities (as technical provisions for contracts where risk is not entirely borne by the policyholders) and the capital requirement appear\r\nvery important issues in Solvency II framework. In this context, we propose a model based on Risk Theory in order to evaluate the capital requirement for mortality and longevity risk. We assume a life portfolio characterized by traditional and with-pro fit products\r\ndivided in several homogeneous generations of contracts. Each cohort includes equal contracts that diff er only by the insured sum with the aim to consider the e ffect of variability\r\ncoeffi cient. Some assumptions allow to obtain closed formulae for the exact characteristics\r\nof demographic profi t distribution regardless of contract types (i.e either with survival or\r\ndeath bene ts). Furthermore Monte-Carlo methods provide the simulated distribution of\r\nmortality and longevity pro fit for each generation. Some case studies show the moments\r\nand the capital requirements for different life portfolios. Finally, further research will regard\r\nboth the aggregation eff ect between several generations and a valuation of liabilities consistent to Solvency II context.