论文标题
二次套期保值和均值变化投资组合选择中一个价格的定律
The law of one price in quadratic hedging and mean-variance portfolio selection
论文作者
论文摘要
一个价格（LOP）的法律广泛地断言，相同的财务流动应以相同的价格命令。我们表明，在正确配制的情况下，LOP是无脱落性的明确定义均值变化投资组合选择框架的最小条件。至关重要的是，本文确定了一种新的机制，通过该机制，LOP可以在不摩擦的情况下连续$ l^2 $设置失败，即“从可预测的停止时间之前进行交易”，这令人惊讶地确定了违反LOP的行为，即使是连续的价格流程。 关闭此漏洞可以在二次背景下给出适用于“资产定价的基本定理”的版本，从而确立了LOP的经济概念与存在本地$ \ scr {e} $的概率特性的等效性。后者在扩展的市场中为所有可融合的主张提供了独特的价格，随后在二次对冲和均值方差投资组合选择中起着重要作用。 从数学上讲，我们为有条件的正方形综合随机变量模块上有条件线性函数的均匀界限原理制定了一种新颖的变体。然后，我们根据固定的局部马丁那样的随机指数来研究此类功能的时段家族的表示。
The law of one price (LOP) broadly asserts that identical financial flows should command the same price. We show that, when properly formulated, LOP is the minimal condition for a well-defined mean-variance portfolio selection framework without degeneracy. Crucially, the paper identifies a new mechanism through which LOP can fail in a continuous-time $L^2$ setting without frictions, namely 'trading from just before a predictable stopping time', which surprisingly identifies LOP violations even for continuous price processes. Closing this loophole allows to give a version of the "Fundamental Theorem of Asset Pricing" appropriate in the quadratic context, establishing the equivalence of the economic concept of LOP with the probabilistic property of the existence of a local $\scr{E}$-martingale state price density. The latter provides unique prices for all square-integrable claims in an extended market and subsequently plays an important role in quadratic hedging and mean-variance portfolio selection. Mathematically, we formulate a novel variant of the uniform boundedness principle for conditionally linear functionals on the $L^0$ module of conditionally square-integrable random variables. We then study the representation of time-consistent families of such functionals in terms of stochastic exponentials of a fixed local martingale.
