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 cadlag 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.
Original language | English (US) |
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Pages (from-to) | 2065-2089 |
Number of pages | 25 |
Journal | SIAM Journal on Control and Optimization |
Volume | 50 |
Issue number | 4 |
DOIs | |
State | Published - 2012 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Applied Mathematics
Keywords
- G-expectation
- Nonlinear martingale
- Replication
- Risk measure
- Second order BSDE
- Superhedging
- Time consistency
- Volatility uncertainty