Estimation and analysis of life annuity premiums with distortion risk measures

Although longevity risk has always been tied to life annuities, the continuous improvement of life expectancy and the current low interest and inflation rates, as well as the less favourable equity returns, have unveiled the magnitude of this risk. Hence, life insurers have to rely on management techniques to reduce their exposure to this risk such as natural hedging, reinsurance or derivatives, though they have limitations. As a consequence, the correct pricing of the longevity exposure has become crucial. Therefore, this study proposes a method for pricing life annuities to create a security margin for insurers against adverse long-term deviations in the survival rates of their insureds. This pricing model consists in applying a distortion operator (PH transform or Wang transform) to the survival distribution function of time-until-death that is used to calculate the life annuity. In addition, a practical example of the proposed model for pricing life annuities is presented. The risk-adjusted premiums for the population from England and Wales are calculated and compared with the non-adjusted-risk premiums. Also, two simulations models are provided to assess the sufficiency of the premiums upon adverse short and long-term deviations in the survival rates