Some properties of nonlinear expectations

HUANG Anqi; ZHOU Jinming; JI Ronglin

doi:10.13471/j.cnki.acta.snus.2019.06.25.2019A050

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Some properties of nonlinear expectations

Research articles | 更新时间：2023-11-01

- Some properties of nonlinear expectations
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 59, Issue 4, Pages: 144-148(2020)
- 作者机构：
  
  1.对外经济贸易大学国际经济贸易学院，北京 100029
  2.安徽大学数学科学学院，安徽合肥 230601
  3.合肥师范学院数学与统计学院，安徽合肥 230601
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2019.06.25.2019A050
  CLC： O211.67
- Published：20 July 2020，
  
  Received：25 June 2019，
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黄安琪,周津名,纪荣林.非线性数学期望的一些性质研究[J].中山大学学报(自然科学版),2020,59(04):144-148.

HUANG Anqi,ZHOU Jinming,JI Ronglin.Some properties of nonlinear expectations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2020,59(04):144-148.
黄安琪,周津名,纪荣林.非线性数学期望的一些性质研究[J].中山大学学报(自然科学版),2020,59(04):144-148. DOI： 10.13471/j.cnki.acta.snus.2019.06.25.2019A050.

HUANG Anqi,ZHOU Jinming,JI Ronglin.Some properties of nonlinear expectations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2020,59(04):144-148. DOI： 10.13471/j.cnki.acta.snus.2019.06.25.2019A050.

摘要

在公理化假设的基本框架下

建立了次线性期望(超线性期望)与一致性风险度量之间的对应关系。进一步地

在对非线性数学期望附加一定的连续性假设的条件下

建立了凸期望(凹期望)与凸风险度量之间的内在联系。

Abstract

Under the axiomatic assumptions for nonlinear expectations and financial risk measures

the relation between sublinear expectations (Resp. superlinear expectations) and coherent risk measures is obtained

respectively.Furthermore

under a natural continuous assumption for the nonlinear expectations

the relationship between convex expectations (Resp. concave expectations) and convex risk measures is also established

respectively.

关键词

非线性数学期望次线性期望凸期望一致性风险度量凸风险度量

Keywords

nonlinear expectationsublinear expectationconvex expectationcoherent risk measureconvex risk measure

references

PARDOUX E, PENG S G. Adapted solution of a backward stochastic differential equation [J].Systems Control Letters,1990,14: 55-61.

PENG S G. BSDE and related g-expectation [J]. in: N El Karoui, L Mazliak (Eds.),Backward Stochastic Differential Equations, in: Pitman Res Notes Math Ser,1997,364: 141-159.

COQUET F, HU Y, MÉMIN J, et al. Filtration consistent nonlinear expectations and related g-expectations [J].Probability Theory and Related Fields,2002,123: 1-27.

PENG S G. Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation [J].Stochastic Processes and their Applications,2008,118: 2223-2253.

CHEN Z J, EPSTEIN L. Ambiguity，risk and asset returns in continuous time [J].Econometrica,2002,70: 1403-1444.

CHEN Z J, KULPERGER R. Minimax pricing and choquet pricing [J].Insurance: Mathematics and Economics,2006,38: 518-528.

HE K, HU M S, CHEN Z J. The relationship between risk measures and choquet expectations in the framework of g-expectations [J].Statistics and Probability Letters,2009,79: 508-512.

HUANG J, JIA G Y. On the minimal members of convex expectations [J].Journal of Mathematical Analysis and Applications,2011,376: 42-50.

JIA G Y. The minimal sublinear expectations and their related properties [J].Science in China Series A: Mathematics,2009,39: 79-87．

JI R L, JIANG L, TIAN D J. On the minimal members of convex expectations with constraints [J].Journal of Inequalities and Applications,2015,191: 1-8.

纪荣林，江龙，石学军. 凸g-期望的若干性质[J].中山大学学报(自然科学版)，2015，54(5)：11-14.

JI R L，JIANG L, SHI X J. Some properties of convex g-expectations [J].Acta Scientiarum Naturalium Universitatis Sunyatseni，2015，54(5)： 11-14.

纪荣林, 周津名. g-期望的凸性及其应用[J]. 中山大学学报(自然科学版),2018,57(5): 127-131.

JI R L, ZHOU J M. Convexity of g-expectations and its application [J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2018,57(5): 127-131.

JIANG L. A necessary and sufficient condition for probability measures dominated by g-expectation [J].Statistics and Probability Letters,2009,79(2): 196-201.

ARTZNER PH, DELBAEN F, EBER J M, et al. Coherent measures of risk [J].Mathematical Finance,1999,4: 203-228.

FÖLLMER H, SCHIED A. Convex measures of risk and trading constraints [J].Finance and Stochastics,2002,6: 429-447.

FRIRRELLI M, ROSAZZA GIANIN E. Putting order in risk measures [J].Journal of Banking and Finance,2002,26: 1473-1486.

ROSAZZA GIANIN E. Risk measures via g-expectations [J].Insurance: Mathematics and Economics,2006,39: 19-34.

JIANG L. Convexity,translation invariance and subadditivity for g-expectations and related risk measures [J].Annals of Applied Probability,2008,18: 245-258.

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JI Ronglin

ZHOU Jinming

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School of Mathematical Sciences, Anhui University

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