Bağımlı Çoklu Yaşam Durumunda Stokastik Ölümlülük Yaklaşımları ve Aktüeryal Fiyatlandırma

Abstract

In this study, stochastic mortality approach is used to calculate the net single premiums of life products. Instantaneous mortality rates of individuals are modelled as time-changed Brownian motion. Here the time change is considered stochastically by means of subordinators. Subordinators are assumed to fit an inverse Gaussian distribution. Thus, the instantaneous mortality rates of individuals are assumed to follow a normal inverse Gaussian distribution. Parameter estimation was performed in such a way that the sum of squared errors between the Dabrowska estimate and the estimate of the joint survival function was minimised. The significance of the model was demonstrated using parametric and non-parametric approaches. The dependency structure between spouses is included in the model through subordinators. Marginal survival probabilities were obtained based on the estimated parameter values. Joint survival probabilities are calculated for both situations based on the assumption that individuals' future life times are dependent and independent. Then, according to the dependency structure of individuals, net single premium values for life annuities and life insurances are obtained in the multiple life situation. Finally, net annual premiums were calculated and the results were compared. Thus, the differences arising in actuarial calculations by taking into account the dependency between individuals are clearly seen.