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Representing filtration consistent nonlinear expectations as $g$-expectations in general probability spaces

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  • Samuel N. Cohen
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    Abstract

    We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous drivers, where both the martingale and the driver terms are permitted to jump, and the martingale representation is infinite dimensional. To establish this result, we show that this domination condition is sufficient to guarantee that the comparison theorem for BSDEs will hold, and we generalise the nonlinear Doob-Meyer decomposition of Peng to a general context.

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    File URL: http://arxiv.org/pdf/1102.5287
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    Paper provided by arXiv.org in its series Papers with number 1102.5287.

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    Date of creation: Feb 2011
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    Handle: RePEc:arx:papers:1102.5287

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