In this thesis, we investigate a pensioner’s gains from access to annuities. We observe a pensioner aged 65, having constant income from social security, having certain amount of pension wealth at age 65. The pensioner optimally decides each year how much of his available assets to consume, to invest into tradable assets, and how much to convert to annuities. Annuities are irreversible investments, once bought they provide income in the later years, but it is not possible to trade annuities any more. The pensioner makes optimal decisions such that the expected discounted utility from future consumption and bequest (if the pensioner has a bequest motive) is maximised. We develop and solve two models for the member of a defined contribution pension scheme in the post–retirement period. The first one is a two assets model with stochastic inflation. We refer to this model as the inflation risk model. The pensioner in the inflation risk model has access to risk less (cash) and risky (equity) investment and to nominal and/or real annuities. The solution of this type of problem using numerical mathematics is presented in detail. We investigate different constraints on annuitisation. The main results presented and analysed are the pensioner’s gains from access to certain class/classes of annuities, and also the pensioner’s optimal asset allocation and annuitisation strategies such that the maximised expected discounted utility from future consumption and bequest is attained. The second model for the pensioner in a defined contribution pension scheme is a three assets model with a stochastic interest rate. We refer to this model as the interest rate risk model. The pensioner in the interest rate risk model has access to risk less (one year bond), low risk (rolling bond with constant duration) and risky (equity) assets, and to annuities. Again, we precisely define the problem mathematically and solve it using numerical mathematics. We present and thoroughly analyse the pensioner’s optimal asset allocation and optimal annuitisation such that his expected discounted utility from consumption and bequest is maximised. Particularly, we investigate in detail the dependence of the results on the value of the interest rate during the year before retirement. After investigating the inflation risk model and interest rate risk model separately, we investigate deeper the new results obtained by introducing a stochastic interest rate. We compare the results obtained in the inflation risk model where the value of the interest rate is constant and the results in the interest rate risk model where the value of the interest rate changes. Particularly, in the interest rate risk model, we investigate deeper the dependence of the results on the value of the interest rate during the year before retirement and on the value of the interest rate during each year before annuitisation and asset allocation during the retirement period.
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