Optimal Consumption, Portfolio, and Retirement Under Implementation Delay

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, kB=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 xR grows by roughly 10%. These results provide policy-relevant insights for retirement systems where procedural lags can distort incentives and reduce welfare.