Representation of dynamic time-consistent convex risk measures with jumps

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.

Keywords

Dynamic convex risk measure dynamic coherent risk measure Poisson random measure backward stochastic differential equations g-expectation minimal penalty term conjugate function