BSDEs, càdlàg martingale problems and orthogonalisation under basis risk.

may, 2016
Publication type:
Paper in peer-reviewed journals
Journal:
SIAM Journal on Financial Mathematics., vol. 7, pp. 308-356
arXiv:
images/icons/icon_arxiv.png 1411.6368
Keywords :
Backward stochastic differential equations; càdlàg martingales; basis risk; Föllmer-Schweizer decomposition; quadratic hedging; martingale problem.
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.
BibTeX:
@article{Laa-Rus-2016,
    author={Ismail Laachir and Francesco Russo },
    title={BSDEs, càdlàg martingale problems and orthogonalisation 
           under basis risk. },
    doi={10.1137/140996239 },
    journal={SIAM Journal on Financial Mathematics. },
    year={2016 },
    month={5},
    volume={7 },
    pages={308--356},
}