Abstract

Mortality rates have shown a gradual and steady decline over the last decades. In this thesis, we propose a stochastic process for the force of mortality. Similarly to Renshaw et al. (1996), the force of mortality will be defined using an exponential function of Legendre polynomials. In order to model perturbations in the force of mortality, we use the approach of Ballotta and Haberman (2006) and add a stochastic process which follows a one-dimensional Ornstein-Uhlenbeck process.

We show how Generalized Linear Models can be used to estimate coefficients of the explanatory variables as well as the value of the coefficient of the Ornstein-Uhlenbeck process. For this purpose, the estimator of this coefficient is obtained by minimizing the residual deviance.

Next we change the structure of the perturbed term in the Ornstein-Uhlenbeck process by replacing Brownian motion with Levy processes. We give some examples to clarify the fitting process and show the advantages of using stochastic forces of mortality. Predictions of the probabilities of death will be investigated to show how the model can be used in actuarial applications. Life annuities are then priced and compared using the proposed model based on Levy processes and the model in Renshaw et al. (1996).

In this thesis, we also reconsider the two-factor stochastic mortality model introduced by Cairns, Blake and Dowd (2006). We first show that the underlying normality assumption of the error terms does not hold for the considered data set. We suggest to model the error terms using bivariate Generalized Hyperbolic distribution that includes four non-Gaussian, fat-tailed distributions. Our empirical analysis shows how the model can provide a better fit for the considered data.

In addition, we try to model age adjusted death rates embedded in the Swiss Re mortality bond using generalized least squares approach. We use the variable length Markov chains (VLMC) model proposed by Machler and Buhlmann (2004) to model the incidence of catastrophic events. The proposed model is compared to the current recognized models in the literature. Finally, we perform a simulation study to estimate the market price of risk that can be used to fairly price the Swiss Re bond.