Martin Keller-Ressel, Eberhard Mayerhofer
Published 2011-11-07, updated 2015-03-12Version 3
We investigate the maximal domain of the moment generating function of affine processes in the sense of Duffie, Filipovi\'{c} and Schachermayer [Ann. Appl. Probab. 13 (2003) 984-1053], and we show the validity of the affine transform formula that connects exponential moments with the solution of a generalized Riccati differential equation. Our result extends and unifies those preceding it (e.g., Glasserman and Kim [Math. Finance 20 (2010) 1-33], Filipovi\'{c} and Mayerhofer [Radon Ser. Comput. Appl. Math. 8 (2009) 1-40] and Kallsen and Muhle-Karbe [Stochastic Process Appl. 120 (2010) 163-181]) in that it allows processes with very general jump behavior, applies to any convex state space and provides both sufficient and necessary conditions for finiteness of exponential moments.
Comments: Published in at http://dx.doi.org/10.1214/14-AAP1009 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Applied Probability 2015, Vol. 25, No. 2, 714-752
Affine Processes
Affine processes on $\mathbb{R}_+^n \times \mathbb{R}^n$ and multiparameter time changes
Affine processes on symmetric cones
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