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

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Author Info
Stephen Satchell (University of Cambridge)
Susan Thorp () (School of Finance and Economics, University of Technology, Sydney)

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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.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp210.pdf
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Publisher Info
Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 210.

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Length: 34
Date of creation: 01 Dec 2007
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Handle: RePEc:uts:rpaper:210

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Related research
Keywords: family extinction; hyperbolic discounting; inter-temporal choice;

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Find related papers by JEL classification:
G0 - Financial Economics - - General
D9 - Microeconomics - - Intertemporal Choice and Growth

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References listed on IDEAS
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  1. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-47, April. [Downloadable!] (restricted)
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  2. David I. Laibson & Andrea Repetto & Jeremy Tobacman, 1998. "Self-Control and Saving for Retirement," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 29(1998-1), pages 91-196. [Downloadable!]
  3. Partha Dasgupta & Eric Maskin, 2005. "Uncertainty and Hyperbolic Discounting," American Economic Review, American Economic Association, vol. 95(4), pages 1290-1299, September. [Downloadable!]
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  4. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-57, July.
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