论文标题
重新审视衍生品的最佳度量
Optimal measure preserving derivatives revisited
论文作者
论文摘要
本文阐明了定价内核单调性与在市场组合上编写的衍生证券的无摩擦市场中存在随机套利的机会之间的关系。关系取决于市场投资组合的回报分布是否满足一种称为适当性的技术条件，这意味着它是无原子的或由有效的许多同样可能的原子组成的。在充分性下，定价内核非单调性等同于存在强烈形式的随机套利形式，涉及以较低的价格对市场组合的分布复制。如果删除了足够的条件，那么这种等价性不再成立，但是定价内核非单调性仍然等于存在较弱形式的随机套利形式，涉及以较低的价格以较低价格的市场投资组合的二阶随机支配地位。获得了保留衍生物的最佳度量的概括，该衍生物以所有二阶随机占主导地位的证券在充分性下以最低成本实现分布复制。
This article clarifies the relationship between pricing kernel monotonicity and the existence of opportunities for stochastic arbitrage in a complete and frictionless market of derivative securities written on a market portfolio. The relationship depends on whether the payoff distribution of the market portfolio satisfies a technical condition called adequacy, meaning that it is atomless or is comprised of finitely many equally probable atoms. Under adequacy, pricing kernel nonmonotonicity is equivalent to the existence of a strong form of stochastic arbitrage involving distributional replication of the market portfolio at a lower price. If the adequacy condition is dropped then this equivalence no longer holds, but pricing kernel nonmonotonicity remains equivalent to the existence of a weaker form of stochastic arbitrage involving second-order stochastic dominance of the market portfolio at a lower price. A generalization of the optimal measure preserving derivative is obtained which achieves distributional replication at the minimum cost of all second-order stochastically dominant securities under adequacy.
