The entropic measure transform |
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Authors: | Renjie Wang Cody Hyndman Anastasis Kratsios |
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Affiliation: | 1. Department of Mathematics and Statistics, Concordia University, Montréal, Québec, Canada, H3H 1M8;2. Department of Mathematics, Eidgenössische Technische Hochschule Zürich, 8092 Zurich, Switzerland |
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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 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 |
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Keywords: | Affine term-structure defaultable bond price forward-backward stochastic differential equations forward price free energy futures price optimal stochastic control quadratic term-structure relative entropy |
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