一致性价格系统与不确定性中性定价
Coherent Price Systems and Uncertainty-Neutral Valuation
摘要：
我们考虑套利定价时所产生的不确定性模型是由一组可能的相互奇异的概率措施的基本问题。在单一概率模型下，不存在套利和存在等价鞅测度之间的本质等价性是一个民间定理，参见Harrison和Kreps（1979）。建立了次线性价格系统的微观经济基础，并给出了一个推广结果。在这种情况下，我们引入了一个先前的依赖概念的市场空间和可行的价格体系。我们将这种扩展与规范改变的概念，等价对称鞅测度集，在一个动态的交易框架下，事先依赖套利。我们证明了存在这样的集合波动率的不确定性是由一个随机微分方程，彭的G-布朗运动驱动。
英文摘要：
We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of arbitrage and the existence of an equivalent martingale measure is a folk theorem, see Harrison and Kreps (1979). We establish a microeconomic foundation of sublinear price systems and present an extension result. In this context we introduce a prior dependent notion of marketed spaces and viable price systems. We associate this extension with a canonically altered concept of equivalent symmetric martingale measure sets, in a dynamic trading framework under absence of prior depending arbitrage. We prove the existence of such sets when volatility uncertainty is modeled by a stochastic differential equation, driven by Peng's G-Brownian motions.
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