The Annals of Applied Probability

Minimal fq-martingale measures for exponential Lévy processes

Monique Jeanblanc, Susanne Klöppel, and Yoshio Miyahara

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Let L be a multidimensional Lévy process under P in its own filtration. The fq-minimal martingale measure Qq is defined as that equivalent local martingale measure for $\mathcal {E}(L)$ which minimizes the fq-divergence E[(dQ/dP)q] for fixed q∈(−∞, 0)∪(1, ∞). We give necessary and sufficient conditions for the existence of Qq and an explicit formula for its density. For q=2, we relate the sufficient conditions to the structure condition and discuss when the former are also necessary. Moreover, we show that Qq converges for q↘1 in entropy to the minimal entropy martingale measure.

Article information

Ann. Appl. Probab., Volume 17, Number 5-6 (2007), 1615-1638.

First available in Project Euclid: 3 October 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G51: Processes with independent increments; Lévy processes
Secondary: 91B28

Lévy processes martingale measures f^q-minimal martingale measure variance minimal martingale measure f-divergence structure condition incomplete markets


Jeanblanc, Monique; Klöppel, Susanne; Miyahara, Yoshio. Minimal f q -martingale measures for exponential Lévy processes. Ann. Appl. Probab. 17 (2007), no. 5-6, 1615--1638. doi:10.1214/07-AAP439.

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