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The cumulant process and Esscher's change of measure

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Author Info
Albert N. Shiryaev () (Steklov Mathematical Institute, Gubkina St. 8, 117966 Moscow, Russia Manuscript)
Jan Kallsen () (Institut für Mathematische Stochastik, Universität Freiburg, Eckerstraße 1, 79104 Freiburg i. Br., Germany)
Abstract

In this paper two kinds of cumulant processes are studied in a general setting. These processes generalize the cumulant of an infinitely divisible random variable and they appear as the exponential compensator of a semimartingale. In a financial context cumulant processes lead to a generalized Esscher transform. We also provide some new criteria for uniform integrability of exponential martingales.

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Publisher Info
Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 6 (2002)
Issue (Month): 4 ()
Pages: 397-428
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Handle: RePEc:spr:finsto:v:6:y:2002:i:4:p:397-428

Note: received: January 2001; final version received: November 2001
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Related research
Keywords: Cumulant process; stochastic logarithm; exponential transform; exponential compensator; exponentially special semimartingale; Esscher transform; uniform integrability;

Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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  1. Liuren Wu, 2004. "Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns," Finance 0401001, EconWPA. [Downloadable!]
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