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Equilibrium consumption and portfolio decisions with stochastic discount rate and time-varying utility functions

Author

Listed:
  • Huiling Wu

    (Central University of Finance and Economics)

  • Chengguo Weng

    (University of Waterloo)

  • Yan Zeng

    (Sun Yat-sen University)

Abstract

This paper studies a multi-period investment–consumption optimization problem with a stochastic discount rate and a time-varying utility function, which are governed by a Markov-modulated regime switching model. The investment is dynamically reallocated between one risk-free asset and one risky asset. The problem is time inconsistent due to the stochastic discount rate. An analytical equilibrium solution is established by resorting to a game theoretical framework. Numerous sensitivity analyses and numerical examples are provided to demonstrate the effects of the stochastic discount rate and time-varying utility coefficients on the decision-maker’s investment–consumption behavior. Our results show that many properties which are satisfied in the classical models do not hold any more due to either the stochastic discount rate or the time-varying utility function.

Suggested Citation

  • Huiling Wu & Chengguo Weng & Yan Zeng, 2018. "Equilibrium consumption and portfolio decisions with stochastic discount rate and time-varying utility functions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(2), pages 541-582, March.
    • Handle: RePEc:spr:orspec:v:40:y:2018:i:2:d:10.1007_s00291-017-0502-2
    DOI: 10.1007/s00291-017-0502-2
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