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On the Distribution of Cash Flows Using Esscher Transforms
Author(s) -
Vyncke D.,
Goovaerts M. J.,
De Schepper A.,
Kaas R.,
Dhaene J.
Publication year - 2003
Publication title -
journal of risk and insurance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.055
H-Index - 63
eISSN - 1539-6975
pISSN - 0022-4367
DOI - 10.1111/1539-6975.t01-1-00065
Subject(s) - logarithm , lévy process , regular polygon , poisson distribution , cash flow , poisson process , inversion (geology) , mathematics , mathematical economics , inverse gaussian distribution , compound poisson process , distribution (mathematics) , econometrics , economics , finance , statistics , mathematical analysis , geology , geometry , paleontology , structural basin
In their seminal paper, Gerber and Shiu (1994) introduced the concept of the Esscher transform for option pricing. As examples they considered the shifted Poisson process, the random walk, a shifted gamma process, and a shifted inverse Gaussian process to describe the logarithm of the stock price. In the present article it is shown how upper and lower bounds in convex order can be obtained when we use these types of models to describe the stochastic accumulation factors for a given cash flow.