2014/11/24 by Ismail Laachir, Laachir, Ismail, Francesco Russo +1
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1411.6368
openalex publication_date 2014/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.