Superhedging and Dynamic Risk Measures under Volatility Uncertainty

Details Superhedging and Dynamic Risk Measures under Volatility Uncertainty Superhedging and Dynamic Risk Measures under Volatility Uncertainty

2010-11-12

arxiv.org/abs/1011.2958v1

Economy

Quantitative Finance

Risk Management

28 pages

Scientific paper

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 c\`adl\`ag 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.

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