Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (5): 995-1003.

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A Conditional Variance for g-Expectation

Hao Tao   

  1. School of Science and Technology, Shandong University of Traditional Chinese Medicine, Jinan 250355
  • Received:2014-08-07 Revised:2015-03-27 Online:2015-10-25 Published:2015-10-25

Abstract:

A conditional variance for g-expectation, named conditional g-variance, is introduced in this paper. The uniqueness theorem for conditional g-variance is proved and the comparison theorem does not hold any more. The sufficient and necessary condition of the property of continuity of conditional g-variance depending on parameters is obtained. At last, we extend conditional g-variance from L4(Ω,FT,P) to L2(Ω,FT) as a continuous mapping in HF1(0,T; R).

Key words: Backward stochastic differential equations, g-Expectation, Conditional g-exp-ectation, g-Variance, Conditional g-variance

CLC Number: 

  • O211.63
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