Discounting And Consumption Over An Uncertain Horizon: Draw-Down Plans For Family Trusts
AbstractIndividuals, 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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Bibliographic InfoPaper provided by Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University in its series CAMA Working Papers with number 2008-02.
Length: 34 pages
Date of creation: Jan 2008
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Other versions of this item:
- Stephen Satchell & Susan Thorp, 2007. "Discounting and Consumption Over an Uncertain Horizon: Draw-Down Plans for Family Trusts," Research Paper Series 210, Quantitative Finance Research Centre, University of Technology, Sydney.
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