Optimal Consumption and Portfolio Choice with No-Borrowing Constraint in the Kim-Omberg Model: The Complete Market Case

Battle Count: 158

Highly relevant for quantitative portfolio management. The paper provides closed-form characterizations of optimal consumption and portfolio strategies under mean-reverting expected excess returns (Kim-Omberg model) with a binding no-borrowing constraint. The free boundary characterization and the economic interpretation of the singular control as a shadow price of the wealth constraint are directly applicable to dynamic asset allocation strategies. The numerical results showing that a stochastic-factor-aware agent systematically outperforms a constant-return agent provide actionable insights for quantitative strategies that exploit return predictability. However, the complete-market assumption and the theoretical nature of the results limit direct implementation without further engineering.

Extremely high complexity. The solution requires: (1) solving a two-dimensional singular stochastic control problem via duality, (2) characterizing a two-dimensional optimal stopping problem with stochastic volatility, (3) establishing Hörmander's condition for hypoellipticity to prove regularity, (4) computing a state-dependent free boundary z*(β), (5) implementing the Skorokhod reflection mechanism for the singular control, and (6) recovering primal optimal strategies via strong duality. The free boundary is not available in closed form and must be computed numerically. The degenerate diffusion structure and stochastic volatility make standard numerical PDE methods challenging to apply.

The paper provides explicit parameter values for numerical illustrations (r=0.03, δ=0.04, ℓ=0.6, γ=1.5, κ=0.25, β̄=0.05, σ_β=0.03, σ=0.18) and describes the simulation methodology (10,000 paths). However, no code repository or supplementary computational materials are provided. The theoretical proofs are fully self-contained, but reproducing the numerical results would require implementing the singular control and optimal stopping algorithms from scratch.