关于半静态交易策略市场的注记
A note on markets with semi-static trading strategies
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中文总结 AI 辅助
本文研究含静态期权的离散时间金融市场套利，引入随机变量小锥概念，证明资产定价基本定理，提供相关实例以论证方法适用性。
中文摘要 AI 辅助
我们研究离散时间金融市场模型中的套利问题，该模型中除了有限多种动态交易资产外，还存在可选择的静态期权。我们引入随机变量小锥的概念，给出市场中可实现头寸依概率闭的充分条件，证明了该语境下的资产定价基本定理，还将考虑效用最大化问题，并提供具有经济意义的无限维小锥实例以论证方法的适用性。
英文摘要
We consider a discrete-time financial market model where, in addition to finitely many dynamically traded assets, there are also (possibly infinitely many) static options to choose from. We introduce the concept of small cones of random variables and present a sufficient condition for the attainable positions in the market to be closed in probability. A fundamental theorem of asset pricing is shown in the present context. Utility maximization will also be considered. We will provide economically meaningful examples of infinite dimensional small cones to demonstrate the pertinence of our approach.
发表机构
- HUN-REN Alfréd Rényi Institute of Mathematics（HUN-REN 阿尔弗雷德·雷尼数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
