Studying old-age population is an active field of research in actuarial science. Espe- cially in the current context of aging population in OECD countries, the actuary has a leading role in managing the related risks. In this thesis, the old-age challenges are adressed considering the pension fund asset liability management (ALM) study as well as the modelling of joint mortality. The thesis contains three chapters.
Chapter 1: Asset Liability Management for Pension Funds: A Survey
Before examining a specific model of ALM for pension funds, it is of interest to review the different methodologies discussed in the literature. In this chapter, the analysis is conducted in two steps. At first, the reader is introduced to the different features of a pension fund. The Swiss system is discussed as an example. In partic- ular, we describe the Swiss three pillars system, emphasize the future reforms and discuss its implications. A brief comparison with some selected OECD countries shows that the Swiss pension funds perform quite well. Secondly, we identify two types of risks in a pension fund: the financial risks and the demographic risks. The ALM framework provides the theoretical background for managing these risks. Considering some key ALM methods, the chapter analyses the advantages and disadvantages of the models.
Chapter 2: On Integrated Chance Constraints in ALM for Pension Funds
The goal of this chapter is to discuss a concrete ALM model using the stochastic programming framework. In this respect, we discuss the role of integrated chance constraints (ICC) as quantitative risk constraints in ALM for pension funds. We de- fine two types of ICC: the one period integrated chance constraint (OICC) and the multiperiod integrated chance constraint (MICC). As their names suggest, the OICC covers only one period whereas several periods are taken into account with the MICC. A multistage stochastic linear programming model is therefore developed for this purpose and a special mention is paid to the modeling of the MICC.
Based on a numerical example, we firstly analyse the effects of the OICC and the MICC on the optimal decisions (asset allocation and contribution rate) of a pension fund. By definition, the MICC is more restrictive and safer compared to the OICC. Secondly, we quantify this MICC safety increase. The results show that although the optimal decisions from the OICC and the MICC differ, the total costs are very close, showing that the MICC might represent a good alternative.
Chapter 3: On Bivariate Lifetime Modeling in Life Insurance Applications
Mortality has an important impact on the pension fund population. Chapter 3 pro- poses a model that describes the lifetimes within a married couple. Insurance and annuity products covering several lives require the modelling of the joint distribu- tion of future lifetimes. In the interest of simplifying calculations, it is common in practice to assume that the future lifetimes among a group of people are indepen- dent. However, extensive research over the past decades suggests otherwise. In this chapter, a copula approach is used to model the dependence between lifetimes within a married couple using data from a large Canadian insurance company. As a novelty, the age difference and the gender of the elder partner are introduced as an argument of the dependence parameter. Maximum likelihood techniques are thus implemented for the parameter estimation. Not only do the results make clear that the correlation decreases with age difference, but also the dependence between the lifetimes is higher when husband is older than wife. A goodness-of-fit procedure is applied in order to assess the validity of the model. Finally, considering several products available on the life insurance market, the paper concludes with practical illustrations.