Discounting and Consumption Over an Uncertain Horizon: Draw-Down Plans for Family Trusts

Stephen Satchell and Susan Thorp
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Stephen Satchell: University of Cambridge

No 210, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: D9 G0 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2007-12-01
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Related works:
Working Paper: DISCOUNTING AND CONSUMPTION OVER AN UNCERTAIN HORIZON: DRAW-DOWN PLANS FOR FAMILY TRUSTS (2008)
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