Superhedging and Dynamic Risk Measures Under Volatility Uncertainty

31 Pages Posted: 15 Jan 2011

See all articles by Marcel Nutz

Marcel Nutz

Columbia University

Halil Mete Soner

ETH Zürich; Swiss Finance Institute

Date Written: November 12, 2010

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.

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

JEL Classification: D81, G11

Suggested Citation

Nutz, Marcel and Soner, Halil Mete, Superhedging and Dynamic Risk Measures Under Volatility Uncertainty (November 12, 2010). Swiss Finance Institute Research Paper No. 10-52, Available at SSRN: https://ssrn.com/abstract=1739781 or http://dx.doi.org/10.2139/ssrn.1739781

Marcel Nutz

Columbia University ( email )

Halil Mete Soner (Contact Author)

ETH Zürich ( email )

Zürichbergstrasse 18
8092 Zurich, CH-1015
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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