Exponential moments of affine processes

Martin Keller-Ressel, Eberhard Mayerhofer

Research output: Contribution to journalArticlepeer-review

Abstract

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

Original languageEnglish
Pages (from-to)714-752
Number of pages39
JournalAnnals of Applied Probability
Volume25
Issue number2
DOIs
Publication statusPublished - 1 Apr 2015
Externally publishedYes

Keywords

  • Affine process
  • Exponential moment
  • Financial modeling
  • Riccati equation

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