发表机构
Sogang University; Kyung Hee University; Sungshin Women’s University（西江大学; 庆熙大学; 诚信女子大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究有限期内福利下限随时间变化时的消费与投资，通过累积乘子转化为障碍问题，分析干预边界存在性、正则性及对偶性，并联系有限承诺与借贷能力。
AI 中文摘要
我们研究了在有限时间范围内，当续期效用必须保持在随时间变化的福利下限之上，且该下限在期末充当最终财富下限时的消费与投资问题。一个累积乘子将该问题简化为抛物型障碍问题。当相对风险厌恶系数大于1时，干预边界在每个内部日期都存在。当该系数小于1时，边界恰好存在于对下限进行折现变换后局部递增并设定严格运行记录的日期，因此边界可能消失并在之后重新出现。我们证明了边界的局部正则性，从障碍解构造对偶值，并验证了最优累积乘子，其矩通过其作为运行上确界的表示得到控制。强对偶性确定了可行财富的精确下端点。在完全市场中的随机收入情况下，该下限成为外部选择权的价值，这将边界与有限承诺和内生的借贷能力联系起来。
英文摘要
We study consumption and investment over a finite horizon when continuation utility must stay above a welfare floor that changes over time, and the floor at the horizon acts as a terminal wealth floor. A cumulative multiplier reduces the problem to a parabolic obstacle problem. When relative risk aversion exceeds one, the intervention boundary exists at every interior date. When it is below one, the boundary exists exactly at the dates where a discounted transformation of the floor is locally increasing and sets a strict running record, so it can disappear and later reenter. We prove local regularity of the boundary, construct the dual value from the obstacle solution, and verify the optimal cumulative multiplier, whose moments are controlled through its representation as a running supremum. Strong duality identifies the exact lower endpoint of feasible wealth. With stochastic income in a complete market, the floor becomes the value of an outside option, which links the boundary to limited commitment and endogenous borrowing capacity.
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