英文标题：
《The Entropic Measure Transform》
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作者：
Renjie Wang, Cody Hyndman and Anastasis Kratsios
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最新提交年份：
2019
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英文摘要：
We introduce the entropic measure transform (EMT) problem for a general process and prove the existence of a unique optimal measure characterizing the solution. The density process of the optimal measure is characterized using a semimartingale BSDE under general conditions. The EMT is used to reinterpret the conditional entropic risk-measure and to obtain a convenient formula for the conditional expectation of a process which admits an affine representation under a related measure. The entropic measure transform is then used provide a new characterization of defaultable bond prices, forward prices, and futures prices when the asset is driven by a jump diffusion. The characterization of these pricing problems in terms of the EMT provides economic interpretations as a maximization of returns subject to a penalty for removing financial risk as expressed through the aggregate relative entropy. The EMT is shown to extend the optimal stochastic control characterization of default-free bond prices of Gombani and Runggaldier (Math. Financ. 23(4):659-686, 2013). These methods are illustrated numerically with an example in the defaultable bond setting.
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中文摘要：
我们引入了一般过程的熵测度变换（EMT）问题，并证明了该问题解的唯一最优测度的存在性。在一般条件下，利用半鞅BSDE刻画了最优测度的密度过程。EMT被用来重新解释条件熵风险测度，并获得一个方便的公式，用于在相关测度下允许仿射表示的过程的条件期望。然后，当资产受到跳跃扩散的驱动时，熵测度变换用于提供可违约债券价格、远期价格和期货价格的新特征。根据EMT对这些定价问题的描述提供了一种经济解释，即收益最大化，并受到通过总相对熵表示的消除金融风险的惩罚。EMT扩展了Gombani和Runggaldier无违约债券价格的最优随机控制特征（Math.Financ.23（4）：659-6862013）。这些方法通过默认键设置中的一个示例进行了数值说明。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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