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摘要翻译：
在Markowitz-Tversky-Kahneman(MTK)参考点的拓扑流形上，引入了局部紧群上风险运算的表示理论。我们确定了（1）风险规避和风险寻求行为的翻转率引起的风险扭转，(2)仿紧流形中的一个结构常数或该扭转的耦合。风险扭转算子通过连续性扩展到审慎和maxmin期望效用(MEU)算子，以及意大利学派引入的其他行为算子。在我们以前的混沌动力系统中，由于概率域的行为旋转，损失厌恶指数是一个未观察到的规范变换；并且参考点在由特殊酉群SU(n)刻画的效用超曲面上是双曲的。本文给出了由变换群诱导的仿紧MTK流形上调和效用函数存在的条件。并利用这些数学对象估计：（1）无穷小切向量的损失厌恶指数；（2）关于MTK基拓扑边界上正则点的布朗运动首次退出时间的经典Dirichlet问题的值函数。
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英文标题：
《Representation Theory for Risk On Markowitz-Tversky-Kahneman Topology》
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作者：
Godfrey Charles-Cadogan
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最新提交年份：
2012
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Mathematics 数学
二级分类：General Topology 一般拓扑
分类描述：Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties
连续统理论，点集拓扑，代数结构空间，基础，维数理论，局部和全局性质
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一级分类：Mathematics 数学
二级分类：Group Theory 群论
分类描述：Finite groups, topological groups, representation theory, cohomology, classification and structure
有限群、拓扑群、表示论、上同调、分类与结构
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一级分类：Mathematics 数学
二级分类：Representation Theory 表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
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英文摘要：
We introduce a representation theory for risk operations on locally compact groups in a partition of unity on a topological manifold for Markowitz-Tversky-Kahneman (MTK) reference points. We identify (1) risk torsion induced by the flip rate for risk averse and risk seeking behaviour, and (2) a structure constant or coupling of that torsion in the paracompact manifold. The risk torsion operator extends by continuity to prudence and maxmin expected utility (MEU) operators, as well as other behavioural operators introduced by the Italian school. In our erstwhile chaotic dynamical system, induced by behavioural rotations of probability domains, the loss aversion index is an unobserved gauge transformation; and reference points are hyperbolic on the utility hypersurface characterized by the special unitary group SU(n). We identify conditions for existence of harmonic utility functions on paracompact MTK manifolds induced by transformation groups. And we use those mathematical objects to estimate: (1) loss aversion index from infinitesimal tangent vectors; and (2) value function from a classic Dirichlet problem for first exit time of Brownian motion from regular points on the boundary of MTK base topology.
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PDF链接：
https://arxiv.org/pdf/1206.2665
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