A note on markets with semi-static trading strategies

2026-08-31

AI Summary

研究了半静态交易策略下的金融市场套利问题，通过引入随机变量小锥概念，并提供其在概率意义下闭合的充分条件。

Abstract

We investigate arbitrage in a discrete-time financial market model where, in addition to finitely many dynamically traded assets, there are also 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.

Problem

• arbitrage
• discrete-time financial market model
• static options
• attainable positions

Innovation

• small cones of random variables
• semi-static trading strategies
• discrete-time financial market model
• arbitrage