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Exponential moments of affine processes. (English) Zbl 1332.60115
Summary: We investigate the maximal domain of the moment generating function of affine processes in the sense of D. Duffie et al. [Ann. Appl. Probab. 13, No. 3, 984–1053 (2003; Zbl 1048.60059)], 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., results by P. Glasserman and K.-K. Kim [Math. Finance 20, No. 1, 1–33 (2010; Zbl 1182.91215)], D. Filipović and E. Mayerhofer [in: Advanced financial modelling. Berlin: de Gruyter. 125–164 (2009; Zbl 1205.91068)] and J. Kallsen and J. Muhle-Karbe [Stochastic Processes Appl. 120, No. 2, 163–181 (2010; Zbl 1185.60045)]) 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.

MSC:
60J25 Continuous-time Markov processes on general state spaces
91G80 Financial applications of other theories
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