Some Mathematical Models for Longevity Risk in the Annuity Market and Pension Funds

Lately, life insurance companies and pension funds confront with longevity risk, namely increased life expectancy. This risk (hazard) and the decrease in the number of employee taxpayers represent major difficulties on the annuity market and pension funds. Therefore, these institutions must provide efficient and suitable means in order to cross-hedge or to transfer part of the longevity risk to reinsurance companies or to financial markets. The markets for longevity derivatives progress, as the insurance industry must satisfy specific requirements related to longevity risk. This paper develops some models for mortality rates and pricing given the longevity risk. As regard forecasting mortality rates, we make some remarks based on various models for the Romanian population. In addition, this paper expands some models for the securitization of longevity bonds or loans. We provide a numerical illustration of the above models.