连续时间下的存储期权与内生商品价格
Storage Options and Endogenous Commodity Prices in Continuous Time
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中文总结 AI 辅助
本研究提出连续时间下存储期权内生定价均衡（ESOE），通过不动点反馈机制刻画商品价格，并给出全局存在性、障碍问题求解及数值验证，揭示需求弹性、折现、折旧和波动性对存储溢价与出售阈值的影响。
中文摘要 AI 辅助
我们研究当出售或持有商品的决定被视为一种嵌入的存储期权时，可存储商品的价格形成机制。价格过程并非外生施加，而是由一个候选价格函数决定需求动态，而由这些动态生成的最优停止值又产生一个新的价格函数。我们将这一反馈机制的不动点称为内生存储期权均衡（ESOE），使用一个独立的缩写来区分此处研究的连续时间构造与经典竞争性存储文献中的平稳理性预期均衡术语。在一个紧致的容许类上，我们在一个透明的漂移-折现条件下建立了全局存在性结果。该论证避免了局部不动点的逐区间扩展，并且不声称由Schauder定理得到唯一性。随后，我们将该均衡刻画为一个非线性障碍问题，并开发了一种具有渐近一致远场边界条件的单调有限差分/策略迭代方法。数值分析将不动点收敛与空间离散误差分开处理，并辅以蒙特卡洛验证、缩放诊断、比较静态分析以及最优出售时间的分布。结果阐明了需求弹性、折现、折旧和波动性如何共同决定存储溢价和出售阈值。
英文摘要
We study the price formation of a storable commodity when the decision to sell or keep the commodity is treated as an embedded storage option. The price process is not imposed exogenously. Instead, a candidate price function determines the demand dynamics, while the optimal stopping value generated by those dynamics produces a new price function. We call a fixed point of this feedback mechanism an endogenous storage-option equilibrium (ESOE), using a separate acronym to distinguish the continuous-time construction studied here from the stationary rational expectations equilibrium terminology of the classical competitive-storage literature. A global existence result is established on a compact admissible class under a transparent drift--discount condition. The argument avoids the interval-by-interval extension of local fixed points and does not claim uniqueness from Schauder's theorem. We then characterize the equilibrium as a nonlinear obstacle problem and develop a monotone finite-difference/policy-iteration method with an asymptotically consistent far-field boundary condition. The numerical analysis separates fixed-point convergence from spatial discretization error and is supplemented by Monte Carlo validation, scaling diagnostics, comparative statics, and the distribution of optimal selling times. The results clarify how demand elasticity, discounting, depreciation, and volatility jointly determine the storage premium and the selling threshold.
发表机构
- Amirkabir University of Technology（阿米尔卡比尔理工大学）
机构由 AI 辅助整理，请以论文原文为准。
