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Dynamic Risk Measures for Anticipated Backward Doubly Stochastic Volterra Integral Equations. 2021

Liangliang Miao, and Zhang Liu, and Yijun Hu
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China.

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.

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