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Hedging contingent claims for a large investor in an incomplete market

Part of: Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

Rainer Buckdahn  and
Ying Hu
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.
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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.

Keywords

Forward-backward stochastic differential equationscontingent claimshedging strategylarge investorconstrained portfoliosincomplete markets

MSC classification

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 1 , March 1998 , pp. 239 - 255
Copyright
Copyright © Applied Probability Trust 1998 

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