稀有状态与长期定价
Rare States and Long-Run Pricing
- University of Sydney（悉尼大学）
- National Graduate Institute for Policy Studies（国立政策研究大学院大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过图论与谱分析，研究可约及几乎可约动态下稀有状态对长期定价的影响，提出定价走廊与类别特定定价率概念，并揭示灾难恢复中偏好与风险因素如何决定主导性与交叉期限。
AI中文摘要：
宏观经济危机是罕见的，但它们可能对资产价格产生巨大影响。由于从正常时期进入危机的概率相对于复苏概率较小，动态过程几乎是可约的：将危机进入概率设为零会使危机状态从正常状态变得不可达。我们发展了在可约和几乎可约动态下长期定价的图论与谱分析。我们表明，在可约极限下，物理动态和定价动态产生相同的经济状态类别和可达性关系，但它们的长期重要性排序不同：分别依据循环性和类别特定定价率。此外，一项索取权的价格仅取决于其定价走廊——从初始状态到支付为正的状态的有向路径上的状态类别——而该走廊内最高的类别特定定价率决定了该索取权的长期定价率。当可约极限走廊排除全局定价主导类别时，我们刻画了恢复稀有转换如何引入该类别的贡献，其权重随着转换变得更稀有而消失。该贡献仅在超过交叉到期期限后才变得主导，该期限随连接路径的稀有性增加而增加，并随主导类别的定价率优势减小而减少。最后，一个基于消费的灾难恢复应用展示了偏好、消费风险、现金流暴露和恢复时机如何共同塑造灾难状态的长期定价主导性和交叉到期期限。
英文摘要：
Macroeconomic crises are rare, yet they can have large effects on asset prices. Because the probability of entering a crisis from normal times is small relative to the probability of recovery, the dynamics are nearly reducible: setting the crisis-entry probability to zero makes crisis states unreachable from normal states. We develop a graph-theoretic and spectral analysis of long-run pricing under reducible and nearly reducible dynamics. We show that, at the reducible limit, physical and pricing dynamics induce the same classes of economic states and accessibility relations, but rank their long-run importance differently: by recurrence and by class-specific pricing rates. Moreover, a claim's price depends only on its pricing corridor---the classes of states lying on directed paths from the initial state to states where the payoff is positive---and the highest class-specific pricing rate within this corridor determines the claim's long-run pricing rate. When the reducible-limit corridor excludes the globally pricing-dominant class, we characterize how restoring rare transitions introduces a contribution from that class with a weight that vanishes as the transitions become rarer. This contribution becomes dominant only beyond a crossover maturity, which increases with the rarity of the connecting paths and decreases with the dominant class's pricing-rate advantage. Finally, a consumption-based disaster-recovery application shows how preferences, consumption risk, cash-flow exposure, and recovery timing jointly shape the long-run pricing dominance of disaster states and crossover maturities.
