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 that admits an affine representation under a related measure. The EMT is then used to provide a new characterization of defaultable bond prices, forward prices and futures prices when a jump‐diffusion drives the asset. The characterization of these pricing problems in terms of the EMT provides economic interpretations as maximizing the 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 & Runggaldier (2013). These methods are illustrated numerically with an example in the defaultable bond setting. The Canadian Journal of Statistics 48: 97–129; 2020 © 2020 Statistical Society of Canada

中文翻译：

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熵测度变换

我们介绍了一般过程的熵度量变换（EMT）问题，并证明了表征该解的唯一最优度量的存在。在一般条件下，使用半martBSDE表征最佳措施的密度过程。EMT用于重新解释有条件的熵风险度量，并为接受相关度量下的仿射表示的过程的条件期望获取便利的公式。然后，当跳跃扩散驱动资产时，EMT将用于提供可违约债券价格，远期价格和期货价格的新特征。用EMT来描述这些定价问题，就可以提供经济上的解释，即使收益最大化，从而可以消除因总的相对熵表示的金融风险而受到的惩罚。研究表明，EMT扩展了Gombani＆Runggaldier（2013）的无违约债券价格的最优随机控制特征。这些方法在默认债券设置中以数字方式举例说明。加拿大统计杂志48：97-129；加拿大统计局。2020©2020加拿大统计学会