EXPONENTIAL MOMENTS OF AFFINE PROCESSES

被引：45
作者：
Keller-Ressel, Martin [1 ]
Mayerhofer, Eberhard [2 ]
机构：
[1] Tech Univ Berlin, Inst Math, Fak 2, D-10623 Berlin, Germany
[2] Dublin City Univ, Sch Math Sci, Dublin 9, Ireland
来源：
ANNALS OF APPLIED PROBABILITY | 2015年 / 25卷 / 02期
关键词：
Affine process; exponential moment; Riccati equation; financial modeling; STOCHASTIC VOLATILITY; TERM STRUCTURE; MODELS; EXPLOSIONS; OPTIONS; JUMPS;
D O I：
10.1214/14-AAP1009
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We investigate the maximal domain of the moment generating function of affine processes in the sense of Duffle, Filipovie 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], Filipovie 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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页码：714 / 752
页数：39
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