Superhedging and Dynamic Risk Measures under Volatility Uncertainty
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.
|Date of creation:||Nov 2010|
|Date of revision:||Jun 2012|
|Publication status:||Published in SIAM Journal of Control and Optimization, 50/4, 2065--2089, (2012)|
|Contact details of provider:|| Web page: http://arxiv.org/|
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