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

Author

Listed:
  • Stephen Satchell

    (University of Cambridge)

  • Susan Thorp

    (University of 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.

Suggested Citation

  • 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.
    • Handle: RePEc:uts:rpaper:210
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    References listed on IDEAS

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    More about this item

    Keywords

    family extinction; hyperbolic discounting; inter-temporal choice;
    All these keywords.

    JEL classification:

    • G0 - Financial Economics - - General
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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