Exponential moments of affine processes

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.

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)

References in corpus (4)

• Affine processes on positive semidefinite matrices
• The affine transform formula for affine jump-diffusions with a general closed convex state space
• Regularity of affine processes on general state spaces
• Pricing and Hedging in Affine Models with Possibility of Default

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