发表机构
Bunkyo Gakuin University（文教学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出有限时域多重停时框架，用于几何随机游走上的美式看跌、俄罗斯及几何平均亚式期权，通过Snell包络和墓地时间编码未行使权利，得到有序最优行权向量，并利用边际值中位数表示导出阈值型规则，同时分析随机到期的影响。
AI 中文摘要
本文发展了一个有限时域的多重停时框架，并将其应用于Cox-Ross-Rubinstein市场中几何随机游走上的三类美式合约：美式看跌期权、俄罗斯期权以及浮动执行价几何平均亚式看跌期权。一般问题通过递归定义的Snell包络表示，未使用的行权权利由墓地时间编码；这产生了一个有序的最优行权向量，而无需要求所有权利都被行使。对于美式看跌期权，连续边际值的中位数表示产生递减的边际值、嵌套的行权区域和单调的行权阈值，而不依赖边际值的凸性。经过适当的状态约简，类似的边际值论证为俄罗斯期权和几何平均亚式期权给出了阈值型的最优行权规则。此外，还纳入了独立的随机到期时间，并确定了其对相应停时区域的影响。
英文摘要
This article develops a finite-horizon multiple-stopping framework and applies it to three American-style contracts on a geometric random walk in a Cox--Ross--Rubinstein market: an American put, a Russian option, and a floating-strike geometric-average Asian put. The general problem is represented by recursively defined Snell envelopes, with unused exercise rights encoded by a cemetery time; this yields an ordered optimal exercise vector without requiring all rights to be exercised. For the American put, a median representation of successive marginal values yields diminishing marginal values, nested exercise regions, and monotone exercise thresholds without relying on convexity of the marginal value. After suitable state reductions, analogous marginal-value arguments give threshold-type optimal exercise rules for the Russian and geometric-average Asian options. Independent random maturity is also incorporated, and its effect on the corresponding stopping regions is identified.
Comments32 pages, 6 figures
