BSDEs, càdlàg martingale problems and orthogonalisation under basis risk.Report as inadecuate




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1 ENSTA ParisTech UMA - Unité de Mathématiques Appliquées 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 $gX T,S T$, 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.

Keywords : Backward stochastic differential equations cadlàg martingales basis risk Föllmer-Schweizer decomposition quadratic hedging martingale problem





Author: Ismail Laachir - Francesco Russo -

Source: https://hal.archives-ouvertes.fr/



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