论文标题
关于在离散时间内资产定价的强大基本定理
On robust fundamental theorems of asset pricing in discrete time
论文作者
论文摘要
本文致力于研究在离散时间和有限的地平线设置中资产定价的鲁棒基本定理。不确定性是通过相同概率空间（可能是无数的）价格过程（可能是无数的）家族来建模的。我们的技术假设是相对于不确定参数的价格过程的连续性。在这种情况下，我们引入了一个新的拓扑框架，该拓扑框架使我们能够在套利定价理论中使用涉及$ l^p $空间，Hahn-Banach分离定理和其他功能分析工具的经典论点。第一个结果是``不健壮的套证条件''的等效性以及新的````强大定价''系统''的存在。第二个结果表明，与其他相关研究不同，二元性二元性和超过策略的存在而没有限制性条件。第三个结果讨论了当前强大设置中的完整性。当其他选择可用于静态交易时，我们可以降低强大的定价系统，从而超过价格。
This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modelled by a (possibly uncountable) family of price processes on the same probability space. Our technical assumption is the continuity of the price processes with respect to uncertain parameters. In this setting, we introduce a new topological framework which allows us to use the classical arguments in arbitrage pricing theory involving $L^p$ spaces, the Hahn-Banach separation theorem and other tools from functional analysis. The first result is the equivalence of a ``no robust arbitrage" condition and the existence of a new ``robust pricing system". The second result shows superhedging dualities and the existence of superhedging strategies without restrictive conditions on payoff functions, unlike other related studies. The third result discusses completeness in the present robust setting. When other options are available for static trading, we could reduce the set of robust pricing systems and hence the superhedging prices.
