Discounting and Consumption Over an Uncertain Horizon: Draw-Down Plans for Family Trusts
Quantitative Finance Research Centre, University of Technology, Sydney Research Paper No. 210
34 Pages Posted: 18 Mar 2008
Date Written: December 2007
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 family trusts facing positive probabilities of extinction at each generation. Using birth statistics for the UK, we compute family extinction probabilities and show that they are well-approximated by a Pareto distribution, hence family trusts will discount hyperbolically. Numerically optimised consumption paths for family trusts with CRRA preferences are decreasing but always higher than for infinitely-lived trusts.
Keywords: family extinction, hyperbolic discounting, inter-temporal choice
JEL Classification: G0, D9
Suggested Citation: Suggested Citation