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Zbl 1035.60040
Fujiwara, Tsukasa; Miyahara, Yoshio
The minimal entropy martingale measures for geometric Lévy processes. (English)
[J] Finance Stoch. 7, No. 4, 509-531 (2003). ISSN 0949-2984; ISSN 1432-1122/e

The authors establish the existence of the minimal entropy martingale measures (MEMMs) for the geometric Lévy processes $\tilde{S}_t$ and show that the MEMM can be defined by means of the Esscher transformation of the return process for $\tilde{S}_t$ which gives an explicit representation of the MEMM. A criterion is given for judging when conditions of the main theorems are fulfilled. For instance, compound Poisson processes, stable processes and variance gamma processes are good enough. It is also proved that MEMM price is the limit of the utility indifference price as the risk aversion parameter tends to 0.
[Yuliya Mishura (Ky\"iv)]

MSC 2000:: *60G44 Martingales with continuous parameter
60G51 Processes with independent increments
60G52 Stable processes
60H20 Stochastic integral equations
60J75 Jump processes
91B24 Price theory and market structure
94A17 Measures of information

Keywords: Geometric Lévy processes; (local) martingale measures; minimal entropy; Esscher transformation; utility indifference price

Cited in: Zbl 1256.60009 Zbl 1180.60061 Zbl 1143.60035

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