Abstract

A model financial market is considered that has an uncertain deterministic evolution of prices in discrete time such that prices of assets evolve under uncertainty described using a priori data about possible increments of prices: they are assumed to lie in given compacta that depend on the prehistory of prices. It is assumed that trading constraints are convex, depend on the prehistory of prices; apply only to risky assets; and allow investment of all amount into a riskless asset. The greatest (in the Pompeiu–Hausdorff metric) perturbation of compacta describing the movement of prices such that the structural stability of the model is preserved (condition of robust no deterministic sure arbitrage with unbounded profit).

中文翻译：

---

无确定利润的稳健无确定性套利条件下的结构稳定性阈值

摘要

考虑到一个模型金融市场，它在离散时间内具有不确定的价格确定性演变，因此资产价格在不确定性下演变，不确定性使用有关价格可能增量的先验数据来描述：假定它们位于给定的契约中，依赖于史前史价格。假定交易约束是凸的，取决于价格的历史。仅适用于风险资产；并允许将所有金额投资到无风险的资产中。紧缩的最大（描述庞贝–豪斯多夫度量）的扰动描述了价格的波动，从而保留了模型的结构稳定性（稳健，无确定性，套利且无边际利润的条件）。