Several inequalities of the $\vec g$-expectation
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摘要: 运用倒向随机微分方程与\,$g$\,-期望的相关性质, 证明了关于\,$g$\,-期望的 \,Markov\,不等式、Chebyshev\,不等式和\,Cantelli\,不等式.
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关键词:
- 倒向随机微分方程 /
- $g$\,-期望 /
- Markov不等式 /
- Chebyshev不等式 /
- Cantelli不等式
Abstract: Based on the related properties of the backward stochastic differential equations and the $g$-expectation, Markov inequality, Chebyshev inequality and Cantelli inequality of the $g$-expectation were proved.-
Key words:
- BSDE /
- $g$-expectation /
- Markov inequality /
- Chebyshev inequality /
- Cantelli inequality
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[1] {1}PARDOUX E, PENG S. Adapted solution of a backward stochasticdifferential equation[J]. Insurance: Systems and Control Letters,1990, 14: 55-61. {2} PENG S G. Backward SDE and related $g$-expectation[G]//EI KAROUI N, MAZLIAK L. Backward Stochastic Differential Equations.Pitman Res Notes Math Ser. Harlow: Longman, 1997, 364: 141-159. {3}JIANG L. Convexity, translation invariance and subadditivity for\,$g$\,expectations and related risk measures[J]. Annals of AppliedProbability, 2008, 18: 245-258. {4}彭实戈. 倒向随机微分方程及其应用[J]. 数学进展, 1997, 26: 97-112. {5}El KAROUI N, PENG S, QUENEZ M C. Baskward stochastic differentialequation in fiance[J]. Mathematical Finance, 1997, 7: 1-71. {6} 李文娟. 非可加概率和倒向随机微分方程的研究~[D]. 山东: 山东大学, 2009. {7}LI W J, CHEN Z J. Laws of large numbers of negatively correlatedrandom variables for capacities[J]. Acta Mathematicae ApplicataeSinica, 2011, 27: 749-760. {8}STIRZAKER David. Probability and Random Variables: A beginner'sguide[M]. Cambridge: Cambridge University Press, 1999. -
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