Affiliations: Department of Finance and Control Sciences, School of Mathematical Sciences, and Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai, China. E-mails: {sjtang, 071018033}@fudan.edu.cn | Graduate Department of Financial Engineering, Ajou University, Suwon, Korea
Note: [] Corresponding author: Shanjian Tang, Department of Finance and Control Sciences, School of Mathematical Sciences, and Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai 200433, China. E-mail: [email protected].
Abstract: For the natural filtration generated by a Brownian motion and a Poisson random measure, the representation of the generator of backward stochastic differential equations and a converse comparison theorem are proved. Moreover, the relation is discussed between g-expectations and dynamic convex and coherent risk measures. The integral representation is discussed for the minimal penalty term of a dynamic convex risk measure.