The aim of this thesis is to investigate how members of Australian superannuation funds can manage risks arising from uncertain security returns and unpredictable mortality so as to ensure a steady income stream during retirement. In chapter 2 we note that the proportion of superannuation assets invested in foreign assets has increased over the past two decades, exposing investors to currency risk. Surveys of superannuation funds verify that most international bond holdings, but not equity holdings, have been hedged for currency risk. We test the mean-variance efficiency of this practice against two alternative hedging strategies: a conventional forward hedge and a selective hedge conditioned on the domestic-foreign interest differential. Implementing optimal hedging results in portfolios whose returns stochastically dominate portfolios constructed under restricted equity hedging, according to our new adaptation of Barrett-Donald (2003) tests. Selective hedging works best for equities and conventional hedging for bonds. Chapter 3 applies a discrete-time Merton (1971) model to questions of optimal decumulation and asset allocation for self-funded retirees drawing down lump-sum retirement benefits. Risk management is taken to revolve around protecting a pre-specified minimum consumption stream. Risk tolerances and lifetimes are allowed to span a range of possibilities. In the case of an agent living to age 90, ideal investment in equity-type assets increases gradually from 27-43 % over remaining life. This is much lower than the 55-60% observed among retirees. Conservative investment strategies are needed to meet consumption goals over long lifetimes. Milevsky and Young (2002, 2003) attribute the reluctance to voluntarily annuitise to a valuable real option to delay annuitisation (RODA). Chapter 4 extends the RODA analysis to the case of HARA preferences. A formula for the optimal timing of annuitisation is derived from the solution to a dynamic stochastic consumption and investment problem with uncertain lifetime. The effect of introducing a consumption floor is to reduce the delay before annuity purchase. As in the CRRA case, delayed annuitisation is associated with optimistic predictions of the Sharpe ratio and divergence between annuity purchaser and provider predictions of mortality.

Assume that we have an~investor who may invests in several risky assets called stocks and in one non-risky asset called bond and that the investor is interested in the expected utility of his/her wealth far in the future. In order to be able to treat the problem, we make several essential simplifying assumptions. First, we assume that the logarithm of the stock market prices is a~multidimensional arithmetic Brownian motion, that the investors pays proportional transaction costs and that the utility function is of a~HARA type. We are able to propose a~strategy that can be called almost optimal in the long run provided that the stock market prices are independent.