IJPAM: Volume 109, No. 2 (2016)


Luca Decarli
Department of Mathematics
University of Trento
via Sommarive, 14-38123 Povo (Trento), ITALY

Abstract. The superhedging problem in a free-arbitrage, incomplete market, is classically solved by mean of the Skorokhod Embedding Problem (SEP) approach, but only in the case of derivatives with time invariant payoff. To avoid such a restriction, we exploit the Monge-Kantorovich (MK) dual approach that turns the starting problem into a problem of stochastic optimization with linear constrain and does not require any time invariant property, in particular the superhedging dual problem for a derivative $\xi$, turns to be its lower bound fair- price for the market. The paper is focused on generalizing the hypothesis on the dynamics of the underlying assets characterizing a given financial market. In particular we extend the results provided by Galichon, Labordere and Touzi in [#!GaLaTa!#], to consider assets whose dynamic admits continuous semimartingale properties. We also provide an alternative dual formulation of the initial problem which allows to apply numerical approximation schemes to the case of super hedging a derivative.

Received: August 2, 2016

AMS Subject Classification: 47N10, 60G40, 60G48, 60H15, 60H35, 62L15, 90-08, 91G20, 91G80

Key Words and Phrases: stochastic optimization, Skorokhod embedding theorem, optimal transportation theory, stochastic hedging problems, stopping times, Monte Carlo simulations

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DOI: 10.12732/ijpam.v109i2.16 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 2
Pages: 429 - 441

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