Superhedging and Dynamic Risk Measures under Volatility Uncertainty

2010/11/30 by Marcel Nutz, H. Mete Soner · 1 citation
Economics, Econometrics and Finance · Mathematics · #math.OC #math.PR #msc:60G44 #msc:60H30 #msc:91B30 #msc:93E20 #q-fin.RM

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published as SIAM Journal of Control and Optimization, 50/4, 2065--2089, (2012) · 31 pages; forthcoming in 'SIAM Journal on Control and Optimization'

arxiv created 2012/06/12 · arxiv updated 2013/06/18

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.

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