IJPAM: Volume 103, No. 1 (2015)

AN INTERVAL OF NO-ARBITRAGE PRICES
FOR AMERICAN CONTINGENT CLAIMS
IN INCOMPLETE MARKETS

Luca Di Persio$^{1}$, Immacolata Oliva$^2$
$^{1,2}$Department of Computer Sciences
University of Verona
Strada le Grazie 15, 37134, Verona, ITALY


Abstract. In this paper we establish an arbitrage-free prices interval for in incomplete financial markets. Such an incompleteness derives from considering uncertain volatility. We use the notion of $G$-expectation, under which the corresponding canonical path is a $G$-, and the related stochastic calculus on suitable stopping time intervals, in a standard financial market characterized by a risk-less asset and one risky stock.

Received: May 26, 2015

AMS Subject Classification: 60G40, 60G44, 91G20, 91G80, 91B25

Key Words and Phrases: American contingent claim, $G$-expectation, pricing, uncertain volatility

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DOI: 10.12732/ijpam.v103i1.11 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 103
Issue: 1
Pages: 133 - 153


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