Multiple Stopping Options on a Geometric Random Walk
Abstract
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.
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BibTeX
@misc{ano2026multiple,
title = {{Multiple Stopping Options on a Geometric Random Walk}},
author = {Katsunori Ano},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30239},
eprint = {2609.30239},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30239},
}
RIS
TY - UNPB
TI - Multiple Stopping Options on a Geometric Random Walk
AU - Katsunori Ano
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30239
UR - https://arxiv.org/abs/2609.30239
AB - 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.
ER -