Finance and Stochastics

, Volume 7, Issue 3, pp 385–402 | Cite as

A semimartingale BSDE related to the minimal entropy martingale measure

  • Michael Mania
  • Marina Santacroce
  • Revaz Tevzadze
Original Paper

Abstract. An incomplete financial market model is considered, where the dynamics of the assets price is described by an \(R^d\)-valued continuous semimartingale. We express the density of the minimal entropy martingale measure in terms of the value process of the related optimization problem and show that this value process is determined as the unique solution of a semimartingale backward equation. We consider some extreme cases when this equation admits an explicit solution.

Key words: Semimartingale backward equation, contingent claim pricing, minimal entropy martingale measure, incomplete markets 
JEL Classification: G10, G12, G13, D52 
Mathematics Subject Classification (2000): 91B28, 60H30, 90C39 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Michael Mania
    • 1
  • Marina Santacroce
    • 2
  • Revaz Tevzadze
    • 3
  1. 1.A. Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Aleksidze St. 1, 380093 Tbilisi, Georgia (e-mail: mania@imath-srv.rmi.acnet.ge) GE
  2. 2.Dipartimento di Scienze Economiche e Metodi Quantitativi, Università degli Studi del Piemonte Orientale A. Avogadro, V. Perrone 18, 28100 Novara, Italy (e-mail: marina.santacroce@eco.unipmn.it) IT
  3. 3.Institute of Cybernetics, Georgian Academy of Sciences, S. Euli St. 5, 380086 Tbilisi, Georgia (e-mail: reztev@yahoo.com) GE

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