A theoretical framework for the pricing of contingent claims in the presence of model uncertainty

2006/07/05 by Laurent Denis, Claude Martini · 3 citations
Mathematics · #math.PR #msc:31C15 #msc:60G44 #msc:60H05

paper · pdf · doi:10.1214/105051606000000169

published as Annals of Applied Probability 2006, Vol. 16, No. 2, 827-852 · Published at http://dx.doi.org/10.1214/105051606000000169 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

arxiv created 2006/07/05 · arxiv updated 2009/12/01

Abstract

The aim of this work is to evaluate the cheapest superreplication price of a general (possibly path-dependent) European contingent claim in a context where the model is uncertain. This setting is a generalization of the uncertain volatility model (UVM) introduced in by Avellaneda, Levy and Paras. The uncertainty is specified by a family of martingale probability measures which may not be dominated. We obtain a partial characterization result and a full characterization which extends Avellaneda, Levy and Paras results in the UVM case.

Cited by

• Stochastic Policy Gradient Methods in the Uncertain Volatility Model
• Reaction-boundary variance and adjoint-consistent local-volatility projection
• Causal Second-Order States under Nondominated Martingale Laws: Restart-Stable Capacity Geometry and Dynamic Transfer