The affine transform formula for affine jump-diffusions with a general closed convex state space

Peter Spreij; Enno Veerman

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arXiv · 1005.1099

The affine transform formula for affine jump-diffusions with a general closed convex state space

Peter Spreij·Enno Veerman

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Abstract

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.

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Peter Spreij, Enno Veerman. 2010-05-06. The affine transform formula for affine jump-diffusions with a general closed convex state space. https://arxiv.org/abs/1005.1099

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