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Time-consistent portfolio optimization

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  • Peng, Ling
  • Kloeden, Peter E.

Abstract

This paper establishes a reusable framework, including a stochastic heterogeneous quasi-hyperbolic (SHQH) discount function, its non-standard Hamilton–Jacobi–Bellman equation (HJB) and its naive and precommitted solutions. To gurantee the broad generalities of the framework, we adopt a game theoretic approach in the sense of refraining from imposing functional specifications. This framework is the first which attains sub-game equilibrium in the presence of heterogeneous preferences (e.g. coexistence of present bias and age-related increases in self-control). As an example, this framework is used to optimize an insurance policy-holder’s asset allocation. The results show: (i) the sophisticated paradigm (formulated via the SHQH HJB) yields higher life insurance investment than the precommitted and naive paradigms (formulated via conventional optimization); (ii) the very instantaneous gratification that composes the resistance to delayed rewards also necessitates the insurance consumption to circumvent this resistance.

Suggested Citation

  • Peng, Ling & Kloeden, Peter E., 2021. "Time-consistent portfolio optimization," European Journal of Operational Research, Elsevier, vol. 288(1), pages 183-193.
    • Handle: RePEc:eee:ejores:v:288:y:2021:i:1:p:183-193
    DOI: 10.1016/j.ejor.2020.05.061
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