Investment Risk Minimization and Optimization of Future Pension Plans

Thesis is a collection of three papers with several contributions to the optimisation of future pension plans for the long-term savers while minimising their investment risk. Since pillar aim is to improve the transparency of the pension funding, we develop investment strategies for individual savers which are easy to understand whilst at the same time performing optimally, or near optimally. Furthermore, all investment prospects are communicated in real terms. Principal investment strategy introduced in the thesis is called probability hedging and it represents modern transition from the unconstrained to constrained allocation strategies. It offers to the savers the option to choose their minimum guarantee for the terminal rewards, subject to a budget constrain and the upper bound which is set, by assumption, to be achieved half of the time. This probability of landing up within the bounds determines the optimal financial hedge for the savers. With particular assumptions of the constant risk premium and the logarithmic utility, our probability hedging strategy drastically simplifies the communication with non-financially educated savers. Further advantages of probability hedging strategy are illustrated on specific long-term investors with different levels of risk-aversion. Additionally, we investigate the effect of the stochastic risk premium on the behaviour of our probability hedging strategy. For such flexible financial modelling we develop the nested simulation algorithm