Retirement income stream products are difficult for consumers to choose because of their high perceived risk, irreversibility, and high expenditure; little opportunity for social learning; and distant consequences. Yet many countries have shifted more responsibility for these choices to...

Individuals, endowments and trusts face uncertain lifetimes. When the planning horizon of an entity is stochastic and Pareto distributed, hyperbolic discounting and time-varying consumption rates are optimal. We derive expressions for the optimal rate of consumption (draw-down) from wealth for...