模型不确定性下套利函数的粘性特征
Viscosity Characterization of the Arbitrage Function under Model Uncertainty
摘要：
我们证明了在一个关于资产的相对风险和协方差结构具有Boghtian不确定性的股票市场模型中，套利函数-定义为使用非预期策略相对于市场可以实现的最高投资回报的倒数，并且在任何容许的市场模型配置下--是一个相关的Hamilton-Jacobi-Bellman（HJB）的黏性解在适当的有界性，连续性和马尔可夫假设下的不确定性结构方程。这个结果推广了Fernholz和Karatzas（2011）的结果，他们将这个套利函数描述为这个HJB方程的柯西问题的经典解，其条件比这里所需的条件强得多。
英文摘要：
We show that in an equity market model with Knightian uncertainty regarding the relative risk and covariance structure of its assets, the arbitrage function -- defined as the reciprocal of the highest return on investment that can be achieved relative to the market using nonanticipative strategies, and under any admissible market model configuration -- is a viscosity solution of an associated Hamilton-Jacobi-Bellman (HJB) equation under appropriate boundedness, continuity and Markovian assumptions on the uncertainty structure. This result generalizes that of Fernholz and Karatzas (2011), who characterized this arbitrage function as a classical solution of a Cauchy problem for this HJB equation under much stronger conditions than those needed here.
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