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
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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}, }