2010/05/06 by Peter Spreij, Spreij, Peter, Enno C.I. Veerman +2
Computer Science · Economics, Econometrics and Finance · Mathematics · #60J60 #91G30 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories #math.PR #msc:60J60 #msc:91G30
paper · pdf · doi:10.48550/arxiv.1005.1099
jumps included
openalex publication_date 2010/05/06 · arxiv created 2010/10/12 · arxiv updated 2010/10/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We establish existence of exponential moments and the validity of the affine transform formula for affine jump-diffusions with a general closed convex state space. This extends known results for affine jump-diffusions with a canonical state space. The key step is to prove the martingale property of an exponential local martingale, using the well-posedness of the associated martingale problem. By analytic extension we obtain the affine transform formula for complex exponentials, in particular for the characteristic function. Our results apply to a wide class of affine processes, including those with a matrix-valued state space, which have recently gained interest in the literature.