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Optimal consumption and investment with welfare constraints

Author

Listed:
  • Junkee Jeon

    (Kyung Hee University)

  • Minsuk Kwak

    (Hankuk University of Foreign Studies)

Abstract

This paper investigates an optimal consumption and investment problem of an economic agent who faces a welfare constraint: the agent does not accept her expected utility (continuation value) to fall below a certain fixed level regardless of the time and state. This optimisation problem involves an infinite number of constraints. Using a duality approach, we transform infinitely many constraints into a single constraint and define a dual problem, which becomes a two-dimensional singular control problem. The dual problem provides its associated Hamilton–Jacobi–Bellman (HJB) equation with a gradient constraint. Under a general class of utility functions, we obtain an explicit solution to the HJB equation and provide optimal strategies by establishing a duality theorem. As an example, we consider hyperbolic absolute risk aversion (HARA) utility which may incorporate a government subsidy or basic support, and provide its solutions and implications.

Suggested Citation

  • Junkee Jeon & Minsuk Kwak, 2024. "Optimal consumption and investment with welfare constraints," Finance and Stochastics, Springer, vol. 28(2), pages 391-451, April.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:2:d:10.1007_s00780-024-00529-1
    DOI: 10.1007/s00780-024-00529-1
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    More about this item

    Keywords

    Consumption and investment; Welfare constraints; General utility; Singular control problem; Duality approach; Dynamic constraints;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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