Abstract
We derive expressions for optimal consumption for family trusts with random wealth and uncertain survival. Using UK birth statistics and the theory of branching processes, we compute size and survival probabilities for single- and multiple-branch families. Survival for a single-branch family is approximated by a Pareto distribution and consumption policies exhibit decreasing discount rates, but multiple-branch families use non-monotonic discount rates. When trust distributions depend on the number of beneficiaries rather than the survival of the whole family unit, spending paths depend on expected membership and the elasticity of intertemporal substitution. We report examples of consumption paths for a range of family trusts with constant relative risk aversion preferences.
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