Abstract

A model is presented of the financial market with a discrete-time uncertain deterministic evolution of prices in which asset prices evolve under uncertainty described using a priori information on possible price increments; i.e., it is assumed that they lie in given compact sets that depend on the prehistory of prices. Trading constraints depending on the history of prices are assumed to be convex, concern only risky assets, and allow all funds to be invested in a risk-free asset. A new geometric criterion is obtained for a robust condition (i.e., the condition ensuring the structural stability of the model) under which there is no guaranteed arbitrage with unlimited profit.

中文翻译：

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无确定套利且收益无限的稳健条件的几何判据

摘要

提出了具有离散时间不确定性价格确定性演变的金融市场模型，其中资产价格在不确定性下演变，不确定性使用关于可能的价格增量的先验信息来描述；即，假设它们位于取决于价格史前的给定紧凑集合中。假定根据价格历史记录的交易约束是凸的，仅涉及风险资产，并且允许将所有资金投资到无风险资产中。对于稳健的条件（即确保模型的结构稳定性的条件）获得了新的几何准则，在稳健的条件下，没有保证的套利和无限的利润。