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Backward Stochastic Differential Equations and Viscosity Solutions of Systems of Semilinear Parabolic and Elliptic PDEs of Second Order

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Stochastic Analysis and Related Topics VI

Part of the book series: Progress in Probability ((PRPR,volume 42))

Abstract

The aim of this article is to present the theory of backward stochastic differential equations, in short BSDEs, and its connections with viscosity solutions of systems of semilinear second order partial differential equations of parabolic and elliptic type, in short PDEs. Linear BSDEs appeared long time ago, both as the equations for the adjoint process in stochastic control, as well as the model behind the Black and Scholes formula for the pricing and hedging of options in mathematical finance. These linear BSDEs can be solved more or less explicitly (see proof of Theorem 1.4).

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Authors
  1. Étienne Pardoux
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Editors and Affiliations

  1. Département Réseaux, École Nationale Supérieure des Télécommunications, 46, rue Barrault, 75634, Paris Cedex 13, France

    Laurent Decreusefond  & Ali Süleyman Üstünel  & 

  2. Dept. of Mathematics, University of Oslo, Box 1053 Blindern, N-0316, Oslo, Norway

    Bernt Øksendal

  3. Central Bureau of Statistics, Norwegian Computing Center, Box 8131 DEP, N-0316, Oslo, Norway

    Jon Gjerde

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Pardoux, É. (1998). Backward Stochastic Differential Equations and Viscosity Solutions of Systems of Semilinear Parabolic and Elliptic PDEs of Second Order. In: Decreusefond, L., Øksendal, B., Gjerde, J., Üstünel, A.S. (eds) Stochastic Analysis and Related Topics VI. Progress in Probability, vol 42. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2022-0_2

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  • DOI: https://doi.org/10.1007/978-1-4612-2022-0_2

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7385-1

  • Online ISBN: 978-1-4612-2022-0

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