发表机构
The Chinese University of Hong Kong; The University of Hong Kong; Shenzhen University（香港中文大学; 香港大学; 深圳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究退休人员委托基金管理人管理资金并需满足最低保障的退休规划问题，提出处理完全非线性HJB方程的新方法，证明经典解存在并刻画辅助方程解的性质，数值实验显示保障约束带来更保守策略且福利损失小。
AI 中文摘要
本文从一个新的视角研究退休规划问题，在该问题中，退休人员将一笔初始一次性资金委托给专业基金管理人。基金被动态管理以提供终身福利，同时满足一项保障，即财富在任何时候都保持在规定的偿付能力水平之上，且福利率保持在最低水平之上。我们将此问题构建为一个连续时间随机控制模型，其中控制变量为福利率和投资组合配置，目标函数包含对福利、管理费和终端遗赠的一般效用函数。由于(i)福利率的控制变量性质；(ii)保障约束；以及(iii)运行中的财富依赖效用这三者的同时影响，标准粘性解和鞅方法等传统方法在此并不直接适用。我们开发了一种新方法，直接处理相关的完全非线性Hamilton-Jacobi-Bellman方程，并确立了经典解的唯一存在性。解决该方程的一个特殊技巧是应用一个复杂的变换，将其转化为半线性辅助方程。一个主要贡献是确立了辅助方程解的存在性，并刻画了其精确的增长、导数和边界行为。这些结果对于建立验证定理和推导最优策略至关重要。此外，数值实验表明，保障约束会诱导更保守的政策，特别是在低财富水平下，同时为财富和福利提供有效的下行保护。相对于无约束框架的相关福利损失仍然很小，这表明将保障纳入退休产品在实践中具有吸引力。
英文摘要
This article studies a retirement planning problem from a new perspective in which a retiree delegates an initial lump sum to a professional fund manager. The fund is managed dynamically to deliver lifelong benefits while satisfying a guarantee that, at all times, wealth remains above a prescribed solvency level and the benefit rate remains above a minimum level. We formulate this problem as a continuous-time stochastic control model, in which the controls are the benefit rate and the portfolio allocation, and the objective incorporates general utility functions over benefits, management fees, and terminal bequest. Conventional approaches such as standard viscosity solution and martingale methods are not immediately applicable here due to the simultaneous influence of (i) the control variable nature of the benefit rate; (ii) the guarantee constraints; and (iii) the running wealth-dependent utility. We develop a new approach that deals directly with the associated fully nonlinear Hamilton-Jacobi-Bellman equation and establish the unique existence of a classical solution. One particular trick for resolving this equation is to apply an intricate transform that diverts the former to a semilinear auxiliary equation. A major contribution is to establish the existence of the solution to the auxiliary equation and characterize its precise growth, derivative, and boundary behavior. These results are crucial for establishing the verification theorems and deriving the optimal strategy. Besides, numerical experiments indicate that guarantee constraints induce more conservative policies, particularly at low wealth levels, while providing effective downside protection for both wealth and benefits. The associated well-being loss relative to the unconstrained framework remains small, suggesting that incorporating guarantees into retirement products is practically appealing.
Comments82 pages, 10 figures
