发表机构
Guangdong College of Commerce; Beijing Normal-Hong Kong Baptist University; The University of Edinburgh; College of William & Mary（广东商学院; 北京师范大学-香港浸会大学联合国际学院; 爱丁堡大学; 威廉玛丽学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对有限乘性系统的边界效应，通过精确格点传播推导最优敞口，发现吸收边界会诱导出表观风险厌恶行为，无需异质性偏好参数即可产生此类行为。
AI 中文摘要
有限乘性系统在达到较低的延续阈值时常停止演化，而标准增长最优基准假设其能无间断延续。我们研究有限时间二元乘性过程，其中预先选择固定敞口，穿越吸收边界的路径被赋予剩余价值。精确格点传播得到最优敞口，其为初始到边界的对数距离、时间跨度及剩余比率的函数。代价高昂的吸收使边界附近的敞口低于无边界Kelly分数，若通过无约束常相对风险厌恶基准解释，这种压缩表现为更高的风险厌恶。当剩余价值趋近边界时，会出现局部高于Kelly的反转，因此吸收边界的几何结构可产生依赖状态的、看似风险厌恶的行为，无需异质性基础偏好参数。
英文摘要
Finite multiplicative systems often cease to evolve when a lower continuation threshold is reached, whereas standard growth-optimal benchmarks assume uninterrupted continuation. We study a finite-horizon multiplicative process in which a fixed exposure is chosen ex ante and paths crossing an absorbing boundary are assigned a residual value. In the continuous-time limit the absorbed objective is available in closed form, and three results follow analytically. Costly absorption compresses exposure below the no-boundary Kelly fraction near the boundary; we prove that this holds strictly whenever the boundary is reachable within the horizon. The dependence on the horizon is non-monotone, and the optimum returns to a finite, cliff-independent long-horizon limit from below or from above according to an exact criterion, at which the threshold is the geometric mean of the residual value and the initial wealth, independently of drift and volatility. When interpreted through an unconstrained constant-relative-risk-aversion benchmark, this compression appears as elevated risk aversion. Exact lattice propagation confirms the analytical predictions without fitted parameters. Absorbing-boundary geometry can therefore generate state-dependent risk-averse-looking behavior without heterogeneous primitive preference parameters.
Comments17 pages,8 figures
