Model-Independent Superhedging Under Portfolio Constraints

27 Pages Posted: 13 Feb 2014 Last revised: 18 Jan 2015

See all articles by Arash Fahim

Arash Fahim

Florida State University - Department of Mathematics

Yu-Jui Huang

University of Colorado at Boulder - Department of Applied Mathematics

Date Written: December 19, 2014

Abstract

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 "fi nite optimal arbitrage pro fit", 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

Fahim, Arash and Huang, Yu-Jui, Model-Independent Superhedging Under Portfolio Constraints (December 19, 2014). Available at SSRN: https://ssrn.com/abstract=2394515 or http://dx.doi.org/10.2139/ssrn.2394515

Arash Fahim

Florida State University - Department of Mathematics ( email )

Tallahassee, FL 32306
United States

Yu-Jui Huang (Contact Author)

University of Colorado at Boulder - Department of Applied Mathematics ( email )

Boulder, CO 80309
United States

HOME PAGE: http://www.yujui-huang.com

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