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

See all articles by Stephen E. Satchell

Stephen E. Satchell

University of Cambridge - Faculty of Economics and Politics

Susan Thorp

University of Sydney Business School; Financial Research Network (FIRN); Centre for International Finance and Regulation (CIFR)

Date Written: December 2007

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

JEL Classification: G0, D9

Suggested Citation

Satchell, Stephen E. and Thorp, Susan, Discounting and Consumption Over an Uncertain Horizon: Draw-Down Plans for Family Trusts (December 2007). Quantitative Finance Research Centre, University of Technology, Sydney Research Paper No. 210 . Available at SSRN: https://ssrn.com/abstract=1106051 or http://dx.doi.org/10.2139/ssrn.1106051

Stephen E. Satchell

University of Cambridge - Faculty of Economics and Politics ( email )

Austin Robinson Building
Sidgwick Avenue
Cambridge, CB3 9DD
United Kingdom
44 (0)1223 335213 (Phone)
44 (0)1223 335475 (Fax)

HOME PAGE: http://www.econ.cam.ac.uk/faculty/satchell/index.h

Susan Thorp (Contact Author)

University of Sydney Business School ( email )

P.O. Box H58
Sydney, NSW 2006
Australia
+61 2 9351 6354 (Phone)

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Centre for International Finance and Regulation (CIFR) ( email )

Level 7, UNSW CBD Campus
1 O'Connell Street
Sydney, NSW 2000
Australia

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