AI 中文总结
该研究针对带破产风险的违约资产出售问题，基于分布构建器方法，通过扩展Skorokhod嵌入问题的结果，构建两类优化问题求解最优出售策略并验证解的性质。
AI 中文摘要
我们在分布构建器（distribution builder）方法的框架下，考虑潜在破产风险时，研究何时出售风险资产最优的问题。该方法允许投资者直接将偏好表达为期望目标分布，无需先指定风险厌恶系数或效用函数。从数学角度看，该问题与Skorokhod嵌入问题密切相关，其目标是通过对扩散过程进行停时处理来获得给定分布。我们在一维扩散过程的一般框架下开展研究，将现有结果扩展至包含破产可能性的情形。我们首先完整刻画了破产前可实现的分布集合，随后构建了两个优化问题以解决原指定分布不可实现或非最优的情况：一是寻找与不可实现分布最接近的可实现分布，二是在原指定分布可实现但非最优时，选择满足一阶随机占优约束的最优可实现分布。我们在扩展的f-散度框架下证明了这些约束凸优化问题解的存在性与唯一性，给出了解的解析刻画并提供了数值示例。
英文摘要
We consider the problem of when it is best to sell a risky asset in the framework of the \textit{distribution builder} approach under the consideration of potential ruin. This approach allows investors to express their preferences directly as a desired target distribution without first specifying a risk aversion or utility function. Mathematically, the problem is closely related to the Skorokhod embedding problem, where the goal is to attain a given distribution by stopping a diffusion process. We work in a general framework of one-dimensional diffusion processes and extend existing results to include the possibility of ruin. We first provide a full characterization of the set of distributions that can be attained before ruin occurs. Then, we formulate two optimization problems that tackle the issue of what to do if the originally specified distribution is either not attainable or not optimal: finding the attainable distribution closest to an unattainable distribution and selecting an optimal attainable distribution under first-order stochastic dominance constraints if the originally specified distribution is attainable, but not optimal. We show existence and uniqueness of solutions to these constrained convex optimization problems in an extended $f$-divergence framework, provide an analytic characterization of solutions and give numerical examples.
Comments33 pages, 2 figures
