A Risk-Theory Model to Assess the Capital Requirement for Mortality and Longevity Risk

Abstract

There is considerable uncertainty regarding the future development of life expectancy that leads to significant change in many fields of the 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 estimation of capital requirement appear very 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-profit products divided in several homogeneous generations of contracts. Each cohort includes equal contracts that differ only by the insured sum with the aim to consider the effect of variability coefficient. Some assumptions allow to obtain closed formulae for the exact characteristics of demographic profit distribution regardless of contract types (i.e either with survival or death benefits). Furthermore Monte-Carlo methods provide the simulated distribution of mortality and longevity profit for each generation. Some case studies show the moments and the capital requirements for different life portfolios. Finally, further research will regard both the aggregation effect between several generations and a valuation of liabilities consistent to Solvency II context.