Model-Independent Superhedging Under Portfolio Constraints
27 Pages Posted: 13 Feb 2014 Last revised: 18 Jan 2015
Date Written: December 19, 2014
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of three parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet possibly less liquid, exotic options, and a dynamic trading strategy in risky assets under certain constraints. By considering the limit order book of each tradable exotic option and employing the Monge-Kantorovich theory of optimal transport, we establish a general superhedging duality, which admits a natural connection to convex risk measures. With the aid of this duality, we derive a model-independent version of the fundamental theorem of asset pricing. The notion "finite optimal arbitrage profit", weaker than no-arbitrage, is also introduced. It is worth noting that our method covers a large class of Delta constraints as well as Gamma constraint.
Keywords: model-independent pricing, robust superhedging, fundamental theorem of asset pricing, portfolio constraints, Monge-Kantorovich optimal transport
JEL Classification: G13, D80
Suggested Citation: Suggested Citation