Stochastic analysis of longevity risk in dependent multiple life annuities

In this study, the AR (1) model was used for the interest rate which is one of the two basic variables that used in calculating the net single premium of the annuity. For the years between 2005-2018, government debt securities, dolar and stocks annual real returns were examined which was obtained from Turkey Statistical Institute (TUIK). These returns are weighted with certain ratios, yielding low and high risk return rate ratios. Then, AR (1) model was created by using these real returns and the real rates of return for the coming years were estimated. For life probabilities of individuals which is the other basic variable, the life probabilities that vary according to age and years obtained from the dynamic life table which is generated from the project made in Turkey called "Creating the Insured and Anüitant Life Tables and Projections". The net single premiums of joint life and last surviving annuities in multiple life annuities have been calculated under the assumptions of independence and dependence between spouses future life times with dynamic and static life probabilities. These values calculated with Monte Carlo simulation method and results are compared. According to the results, in case of dependence of life time, the net single premium of the joint life whole annuity is higher than that of independence, whereas the survivorship whole annuity gives lower results under dependency than the net single premium in independence case. The reason is when positive dependence is accepted among the spouses, the possibility of life increases if the other spouse is alive, while the possibility of life decreases if the other spouse is dead. If the interest rate is stochastic, the net single premiums show higher results. In annuity calculations made with tables that includes the risk of longevity, the net single premiums are higher than the net single premiums calculated according to the table without the risk of longevity. Keywords: Longevity risk, Monte-Carlo Simulation, Multiple Life Annuities, Stochastic Return, Stochastic Mortality, Autoregressive Model, Copula Dependency