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Harnack inequality and no-arbitrage bounds for self-financing portfolios

Author

Listed:
  • Carciola, Alessandro
  • Pascucci, Andrea
  • Polidoro, Sergio

Abstract

We give a direct proof of the Harnack inequality for a class of Kolmogorov operators associated with a linear SDE and we find the explicit expression of the optimal Harnack constant. We discuss some possible implication of the Harnack inequality in finance: specifically we infer no-arbitrage bounds for the value of self-financing portfolios in terms of the initial wealth.

Suggested Citation

  • Carciola, Alessandro & Pascucci, Andrea & Polidoro, Sergio, 2009. "Harnack inequality and no-arbitrage bounds for self-financing portfolios," MPRA Paper 15665, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:15665
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    File URL: https://mpra.ub.uni-muenchen.de/15665/1/MPRA_paper_15665.pdf
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    Citations

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    Cited by:

    1. Wanxiao Tang & Jun Zhao & Peibiao Zhao, 2019. "Geometric No-Arbitrage Analysis in the Dynamic Financial Market with Transaction Costs," JRFM, MDPI, vol. 12(1), pages 1-17, February.

    More about this item

    Keywords

    Harnack inequality; no-arbitrage principle; self-financing portfolio; Kolmogorov equation; linear stochastic equation;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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