BSDEs, càdlàg martingale problems and orthogonalisation under basis risk. - Archive ouverte HAL Access content directly
Journal Articles SIAM Journal on Financial Mathematics Year : 2016

BSDEs, càdlàg martingale problems and orthogonalisation under basis risk.

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.
Fichier principal
Vignette du fichier
BSDEandMartingaleProblemFinalMarch2016.pdf (576.34 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01086227 , version 1 (23-11-2014)
hal-01086227 , version 2 (20-03-2016)

Identifiers

Cite

Ismail Laachir, Francesco Russo. BSDEs, càdlàg martingale problems and orthogonalisation under basis risk.. SIAM Journal on Financial Mathematics, 2016, 7, pp.308-356. ⟨10.1137/140996239⟩. ⟨hal-01086227v2⟩
474 View
329 Download

Altmetric

Share

Gmail Facebook X LinkedIn More