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2007.175: The cumulant process and Esscher's change of measure

2007.175: Jan Kallsen and Albert N. Shiryaev (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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DOI: 10.1007/s007800200069


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 2000 > 60 Probability theory and stochastic processes
MSC 2000 > 91 Game theory, economics, social and behavioral sciences
MIMS number:2007.175
Deposited By:Mrs Louise Healey
Deposited On:19 November 2007

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