Superhedging and Dynamic Risk Measures Under Volatility Uncertainty

Abstract:     
We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging problem. The superhedging strategy is obtained from a representation similar to the optional decomposition. Furthermore, we prove an optional sampling theorem for the nonlinear martingale and characterize it as the solution of a second order backward SDE. The uniqueness of dynamic extensions of static sublinear expectations is also studied.

Number of Pages in PDF File: 31

Keywords: Volatility Uncertainty, Risk Measure, Time Consistency, Nonlinear Martingale, Superhedging, Replication, Second Order BSDE, G-Expectation AMS 2000 Subject

JEL Classification: D81, G11

working papers series