Optimal stopping under volatility ambiguity

• 成果类型: Article
• 署名作者: Cao, Wenbin; Chen, Xiaowei; Ye, Yinghui; Yuan, Wei
• 署名单位: Texas State University System; Sam Houston State University; Nankai University; Sun Yat Sen University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2026.106244
• 发表日期: 2026
• 关键词: differential-equations driven; irreversible investment; nonlinear expectations; Information revelation; incomplete contracts; uncertainty; RISK; MODEL; search; procurement

摘要

We develop a verification theorem for infinite-horizon optimal stopping under G-Brownian motion and apply it to several stopping problems of economic interest. The theorem gives sufficient conditions under which a candidate solution to a system of variational inequalities is the value function under volatility, covariance, or joint drift-volatility ambiguity. In the canonical irreversible investment problem, volatility ambiguity advances investment because the worst-case scenario selects the lowest feasible volatility for a convex continuation value. Ambiguity about volatility therefore acts in the opposite direction from volatility itself, which postpones investment. In other environments, worst-case volatility can vary with the state, alter project relevance, create bilateral valuation wedges, shorten search, and change two-dimensional investment payoffs through covariance and correlation ambiguity. A common convexity-based mechanism drives these results: volatility ambiguity changes the perceived dispersion of future outcomes, whereas drift ambiguity acts through monotonicity.