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Optimal Consumption with Intertemporal Substitution under Knightian Uncertainty

Author

Listed:
  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Li, Hanwu

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We study an intertemporal consumption and portfolio choice problem under Knightian uncertainty in which agent's preferences exhibit local intertemporal substitution. We also allow for market frictions in the sense that the pricing functional is nonlinear. We prove existence and uniqueness of the optimal consumption plan, and we derive a set of sufficient first-order conditions for optimality. With the help of a backward equation, we are able to determine the structure of optimal consumption plans. We obtain explicit solutions in a stationary setting in which the financial market has different risk premia for short and long positions.

Suggested Citation

  • Ferrari, Giorgio & Li, Hanwu & Riedel, Frank, 2020. "Optimal Consumption with Intertemporal Substitution under Knightian Uncertainty," Center for Mathematical Economics Working Papers 641, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:641
    as

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    References listed on IDEAS

    as
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    Keywords

    Hindy-Huang-Kreps preferences; Knightian uncertainty; g-expectation; ambiguity aversion; singular stochastic control;
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