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Hedging contingent claims for a large investor in an incomplete market

Published online by Cambridge University Press:  01 July 2016

Rainer Buckdahn*
Affiliation:
Université de Bretagne Occidentale
Ying Hu*
Affiliation:
Université Blaise Pascal
*
Postal address: Département de Mathématiques, Université de Bretagne Occidentale, 29285 Brest Cédex, France.
∗∗ Postal address: Laboratoire de Mathématiques Appliquées, Université Blaise Pascal - Clermont-Ferrand II, 63177 Aubière Cédex, France.

Abstract

In this paper we study the problem of pricing contingent claims for a large investor (i.e. the coefficients of the price equation can also depend on the wealth process of the hedger) in an incomplete market where the portfolios are constrained. We formulate this problem so as to find the minimal solution of forward-backward stochastic differential equations (FBSDEs) with constraints. We use the penalization method to construct a sequence of FBSDEs without constraints, and we show that the solutions of these equations converge to the minimal solution we are interested in.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 1998 

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