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BSDEs, càdlàg martingale problems and orthogonalisation under basis risk.

Ismail Laachir 1, 2 Francesco Russo 1
2 Lab-STICC_UBS_CACS_IAS
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : The aim of this paper is to introduce a new formalism for the deterministic analysis associated with backward stochastic differential equations driven by general càdlàg martingales. When the martingale is a standard Brownian motion, the natural deterministic analysis is provided by the solution of a semilinear PDE of parabolic type. A significant application concerns the hedging problem under basis risk of a contingent claim $g(X_T,S_T)$, where $S$ (resp. $X$) is an underlying price of a traded (resp. non-traded but observable) asset, via the celebrated Föllmer-Schweizer decomposition. We revisit the case when the couple of price processes $(X,S)$ is a diffusion and we provide explicit expressions when $(X,S)$ is an exponential of additive processes.
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https://hal.inria.fr/hal-01086227
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Submitted on : Sunday, March 20, 2016 - 3:07:06 PM
Last modification on : Tuesday, December 8, 2020 - 9:45:26 AM
Long-term archiving on: : Tuesday, June 21, 2016 - 10:14:43 AM

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  • HAL Id : hal-01086227, version 2
  • ARXIV : 1411.6368

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Ismail Laachir, Francesco Russo. BSDEs, càdlàg martingale problems and orthogonalisation under basis risk.. 2016. ⟨hal-01086227v2⟩

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