论文标题
与子集的晶格相关的多面体，并最大程度地提高了随机变量的期望
Polytopes associated with lattices of subsets and maximising expectation of random variables
论文作者
论文摘要
本论文源自有关基于二项式模型的每个资产的欧洲呼叫选项的价值，涉及与欧洲呼叫期权计算价值有关的问题。该模型导致了一个有趣的polytopes $ p（b）$与电源集$ \ nathcal {l} = \ wp \ {1，\ dots，m \} $相关的，并由$ b \ in \ mathbb {r}^m $进行参数化，每个都是$ \ mathcal concloyapery poctionality prominate ocy octosibality promipational in $ \ mathcal} $ {对于每个非空的$ p（b）$，结果是$ \ mathcal {l}^n $的一系列概率措施，并且，给定一个函数$ f \ colon \ colon \ colon \ colon \ mathcal {l}^n \ to \ mathbb {r {r} $，我们的目标是在这些概率上找到最大程度地提高$ $的可能性。在本文中，我们确定了一个此类功能$ f $的家族，其所有期望在某些条件下最大化（在某些条件下将其最小化）通过相同的{\ em Product}概率度量，该概率度量由$ p（b）$称为超级vertex的杰出顶点定义（supervertex（subververx）。欧洲呼叫期权的回报属于这个功能家族。
The present paper originated from a problem in Financial Mathematics concerned with calculating the value of a European call option based on multiple assets each following the binomial model. The model led to an interesting family of polytopes $P(b)$ associated with the power-set $\mathcal{L} = \wp\{1,\dots,m\}$ and parameterized by $b \in \mathbb{R}^m$, each of which is a collection of probability density function on $\mathcal{L}$. For each non-empty $P(b)$ there results a family of probability measures on $\mathcal{L}^n$ and, given a function $F \colon \mathcal{L}^n \to \mathbb{R}$, our goal is to find among these probability measures one which maximises (resp. minimises) the expectation of $F$. In this paper we identify a family of such functions $F$, all of whose expectations are maximised (resp. minimised under some conditions) by the same {\em product} probability measure defined by a distinguished vertex of $P(b)$ called the supervertex (resp. the subvertex). The pay-offs of European call options belong to this family of functions.
