The cumulant process and Esscher's change of measure

Kallsen, Jan and Shiryaev, Albert N. (2002) The cumulant process and Esscher's change of measure. Finance and Stochastics, 6 (4). pp. 397-428. ISSN 1432-1122

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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.

Item Type: Article
Uncontrolled Keywords: Cumulant process, stochastic logarithm, exponential transform, exponential compensator, exponentially special semimartingale, Esscher transform, uniform integrability
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
MSC 2010, the AMS's Mathematics Subject Classification > 91 Game theory, economics, social and behavioral sciences
Depositing User: Ms Lucy van Russelt
Date Deposited: 19 Nov 2007
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/912

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