Exponential moments of affine processes

2011/11/30 by Martin Keller-Ressel, Eberhard Mayerhofer · 1 citation
Mathematics · #math.PR

paper · pdf · doi:10.1214/14-aap1009

published as Annals of Applied Probability 2015, Vol. 25, No. 2, 714-752 · 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)

arxiv created 2015/03/12 · arxiv updated 2015/03/13

Abstract

We investigate the maximal domain of the moment generating function of affine processes in the sense of Duffie, Filipović 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], Filipović 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.

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