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Optimal annuitization and asset allocation under linear habit formation

Author

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  • Guan, Guohui
  • Liang, Zongxia
  • Ma, Xingjian

Abstract

This paper studies the optimal consumption-investment-annuitization problem for a retiree with linear consumption habits. We explore the effect of consumption habits on the decision to annuitize when annuities are purchased as a lump sum. The problem is formulated as a combined stopping-control problem. We derive optimal annuitization time, investment, and consumption strategies by a generalized dual method and habit reduction method. We investigate the influence of various factors on the annuitization time and derive optimal annuitization time, which is a barrier strategy. The numerical simulations reveal several interesting results. Our results demonstrate that risk aversion, subjective hazard rate, and consumption habits all play a role in shaping annuitization decisions. Furthermore, we offer a new explanation for the rarity of voluntary annuitization among retirees.

Suggested Citation

  • Guan, Guohui & Liang, Zongxia & Ma, Xingjian, 2024. "Optimal annuitization and asset allocation under linear habit formation," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 176-191.
    • Handle: RePEc:eee:insuma:v:114:y:2024:i:c:p:176-191
    DOI: 10.1016/j.insmatheco.2023.11.007
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    More about this item

    Keywords

    Linear habit formation; Stopping-control problem; Annuitization; Dual methods; Variational inequalities;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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