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The Entropic Measure Transform

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  • Renjie Wang
  • Cody Hyndman
  • Anastasis Kratsios

Abstract

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.

Suggested Citation

  • Renjie Wang & Cody Hyndman & Anastasis Kratsios, 2015. "The Entropic Measure Transform," Papers 1511.06032, arXiv.org, revised Feb 2019.
    • Handle: RePEc:arx:papers:1511.06032
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