Dynamic Risk Measures for Anticipated Backward Doubly Stochastic Volterra Integral Equations

Liangliang Miao; Zhang Liu; Yijun Hu

doi:10.3390/e23121580

Dynamic Risk Measures for Anticipated Backward Doubly Stochastic Volterra Integral Equations

Entropy (Basel). 2021 Nov 26;23(12):1580. doi: 10.3390/e23121580.

Authors

Liangliang Miao¹, Zhang Liu², Yijun Hu¹

Affiliations

¹ School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China.
² School of Computer and Information Engineering, Jiangxi Agricultural University, Nanchang 330045, China.

Abstract

Inspired by the consideration of some inside and future market information in financial market, a class of anticipated backward doubly stochastic Volterra integral equations (ABDSVIEs) are introduced to induce dynamic risk measures for risk quantification. The theory, including the existence, uniqueness and a comparison theorem for ABDSVIEs, is provided. Finally, dynamic convex risk measures by ABDSVIEs are discussed.

Keywords: anticipated backward doubly stochastic Volterra integral equations; comparison theorems; dynamic risk measures.

Abstract

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