BSDEs, c{\`a}dl{\`a}g martingale problems and orthogonalisation under basis risk

Ismail Laachir; Francesco Russo

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arXiv · 1411.6368

BSDEs, c{\`a}dl{\`a}g martingale problems and orthogonalisation under basis risk

Ismail Laachir·Francesco Russo

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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 c{\`a}dl{\`a}g 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 F{\"o}llmer-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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BibTeX RIS

Ismail Laachir, Francesco Russo. 2014-11-24. BSDEs, c{\`a}dl{\`a}g martingale problems and orthogonalisation under basis risk. https://arxiv.org/abs/1411.6368

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