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Multidimensional g-expectations and Risk Measures
xu yuhong * #
Department of Mathematics, China University of Mining and Technology
*Correspondence author
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Funding: none
Opened online: 2 October 2008
Accepted by: none
Citation: xu yuhong.Multidimensional g-expectations and Risk Measures[OL]. [ 2 October 2008] http://en.paper.edu.cn/en_releasepaper/content/24507
 
 
This paper proposes a notion of multidimensional g-expectations which provide a multidimensional version of nonlinear expectations. By a technical result on explicit expressions for the comparison theorem of multidimensional backward stochastic differential equations, necessary and sufficient conditions are given for the constancy, monotonicity and positivity properties of multidimensional g-expectations; we also prove that a multidimensional risk measure introduced by multidimensional g-expectation is concave if and only if the generator g satisfies a concave-like condition.
Keywords:Backward stochastic differential equation;g-expectation; risk measure
 
 
 

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