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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
ISSN
1572-9176
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Volume 7, Issue 4

Issues

A Semimartingale Bellman Equation and the Variance-Optimal Martingale Measure

M. Mania
  • A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., Tbilisi 380093, Georgia. E-mail:
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/ R. Tevzadze
  • Institute of Cybernetics, Georgian Academy of Sciences, 5, S. Euli St., Tbilisi 380086, Georgia. E-mail:
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Published Online: 2010-02-23 | DOI: https://doi.org/10.1515/GMJ.2000.765

Abstract

We consider a financial market model, where the dynamics of asset prices is given by an Rm -valued continuous semimartingale. Using the dynamic programming approach we obtain an explicit description of the variance optimal martingale measure in terms of the value process of a suitable problem of an optimal equivalent change of measure and show that this value process uniquely solves the corresponding semimartingale backward equation. This result is applied to prove the existence of a unique generalized solution of Bellman's equation for stochastic volatility models, which is used to determine the variance-optimal martingale measure.

Key words and phrases:: Backward semimartingale equation; incomplete markets; contingent claim pricing; variance-optimal martingale measure; the Bellman equation

About the article

Received: 2000-06-26

Published Online: 2010-02-23

Published in Print: 2000-12-01


Citation Information: Georgian Mathematical Journal, Volume 7, Issue 4, Pages 765–792, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/GMJ.2000.765.

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