# The Entropic Measure Transform

arXiv: https://arxiv.org/abs/1511.06032 · HTML: https://mlsanity.com/paper/1511.06032/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2015.

## Built on by (most cited first, 3 of 3)

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- [Filtered not Mixed: Stochastic Filtering-Based Online Gating for Mixture of Large Language Models](https://mlsanity.com/paper/2406.02969/) (2024)
- [LoRA Fine-Tuning Without GPUs: A CPU-Efficient Meta-Generation Framework for LLMs](https://mlsanity.com/paper/2507.01806/) (2025)

## Abstract (arXiv)

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.