带交易成本与模型不确定性的离散资产定价：含与不含卖空约束的情形
Discrete asset pricing under transaction costs and model uncertainty with and without short-sale constraints
浏览论文内容
中文总结 AI 辅助
该研究针对含交易成本与模型不确定性的离散时间资产定价，建立了含/不含卖空约束的资产定价基本定理，引入稳健上鞅一致价格系统并通过示例验证相关条件的充分性。
中文摘要 AI 辅助
我们研究存在买卖价差与模型不确定性的离散时间资产定价问题。概率测度族通过其支撑集的并集纳入无套利条件。在单期框架下，我们建立了含卖空约束与不含卖空约束的资产定价基本定理：无约束市场中，无套利等价于存在全支撑鞅一致价格系统；在卖空约束下，鞅条件被上鞅条件取代。随后我们将这些结果扩展至有限多期树模型，允许初始信息非平凡，因此初始交易成本与估值边界可依赖初始状态，相应不等式以条件形式表述。最后，针对一类定价测度，我们引入上下稳健上鞅一致价格系统，证明无套利意味着下系统存在，而上系统的存在是无套利的充分条件；一个两状态示例表明仅下条件并不充分。
英文摘要
We study discrete-time asset pricing with bid-ask spreads and model uncertainty. The family of probability measures enters the no-arbitrage condition through the union of its supports. In the single-period setting, we establish fundamental theorems of asset pricing with and without short-sale constraints. In the unconstrained market, no arbitrage is equivalent to the existence of a full-support martingale consistent price system. Under short-sale constraints, the martingale condition is replaced by a supermartingale condition. We then extend these results to a finite multi-period tree. The initial information is allowed to be nontrivial, so the initial trading cost and valuation bounds may depend on the initial state, and the corresponding inequalities are formulated conditionally. Finally, for a family of pricing measures, we introduce lower and upper robust supermartingale consistent price systems. We show that no arbitrage implies the existence of a lower system, while the existence of an upper system is sufficient for no arbitrage. A two-state example shows that the lower condition alone is not sufficient.
