Model-independent superhedging under portfolio constraints

Arash Fahim () and Yu-Jui Huang ()
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Arash Fahim: Florida State University
Yu-Jui Huang: Dublin City University

Finance and Stochastics, 2016, vol. 20, issue 1, No 2, 81 pages

Abstract: Abstract In a discrete-time market, we study model-independent superhedging where 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 and gamma constraints.

Keywords: Model-independent pricing; Robust superhedging; Limit order book; Fundamental theorem of asset pricing; Portfolio constraints; Monge–Kantorovich optimal transport; 91G20; 91G80 (search for similar items in EconPapers)
JEL-codes: C61 G13 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s00780-015-0284-9

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