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Martingale representation for Poisson processes with applications to minimal variance hedging


Reference:

Last, G. and Penrose, M. D., 2011. Martingale representation for Poisson processes with applications to minimal variance hedging. Stochastic Processes and their Applications, 121 (7), pp. 1588-1606.

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http://dx.doi.org/10.1016/j.spa.2011.03.014

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Abstract

We consider a Poisson process n on a measurable space equipped with a strict partial ordering, assumed to be total almost everywhere with respect to the intensity measure of n. We give a Clark-Ocone type formula providing an explicit representation of square integrable martingales (defined with respect to the natural filtration associated with n), which was previously known only in the special case, when is the product of Lebesgue measure on R+ and a -finite measure on another space X. Our proof is new and based on only a few basic properties of Poisson processes and stochastic integrals. We also consider the more general case of an independent random measure in the sense of Ito of pure jump type and show that the Clark-Ocone type representation leads to an explicit version of the Kunita-Watanabe decomposition of square integrable martingales. We also find the explicit minimal variance hedge in a quite general financial market driven by an independent random measure.

Details

Item Type Articles
CreatorsLast, G.and Penrose, M. D.
DOI10.1016/j.spa.2011.03.014
Related URLs
URLURL Type
http://arxiv.org/abs/1001.3972Free Full-text
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code23939

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