The cumulant process and Esscher's change of measure

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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Year of publication:	2002-08-19
Authors:	Shiryaev, Albert N. ; Kallsen, Jan
Published in:	Finance and Stochastics. - Springer. - Vol. 6.2002, 4, p. 397-428
Publisher:	Springer
Subject:	Cumulant process \| stochastic logarithm \| exponential transform \| exponential compensator \| exponentially special semimartingale \| Esscher transform \| uniform integrability

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Extent:	application/pdf
Type of publication:	Article
Notes:	received: January 2001; final version received: November 2001
Classification:	G13 - Contingent Pricing; Futures Pricing ; D52 - Incomplete Markets
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005759605