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Optimal Consumption, Portfolio, and Retirement Under Implementation Delay

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  • Geonwoo Kim

    (School of Natural Sciences, Seoul National University of Science and Technology, Seoul 01811, Republic of Korea
    These authors contributed equally to this work.)

  • Junkee Jeon

    (Department of Applied Mathematics, Kyung Hee University, Yongin 17104, Republic of Korea
    These authors contributed equally to this work.)

Abstract

We develop a continuous-time model of optimal consumption, portfolio allocation, and early retirement that, to our knowledge, is the first to incorporate an implementation delay —a fixed lag δ between the retirement decision and the actual cessation of labor and income. Using a dual-martingale approach, we obtain closed-form solutions and quantify how δ affects optimal behavior. For example, when δ increases from 0.5 to 2 years (baseline parameters: β = 0.04 , r = 0.02 , μ = 0.08 , σ = 0.2 , γ = 3 , k B = 0.3 , and ε = 1 ), optimal pre-retirement consumption rises by approximately 7%, the risky asset share falls by about 5 percentage points, the expected retirement time increases by over 1 year, and the retirement wealth threshold x R grows by roughly 10%. These results provide policy-relevant insights for retirement systems where procedural lags can distort incentives and reduce welfare.

Suggested Citation

  • Geonwoo Kim & Junkee Jeon, 2025. "Optimal Consumption, Portfolio, and Retirement Under Implementation Delay," Mathematics, MDPI, vol. 13(17), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2704-:d:1730346
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