IDEAS home Printed from https://ideas.repec.org/p/pav/wpaper/123.html
   My bibliography  Save this paper

Finitely Additive Equivalent Martingale Measures

Author

Listed:
  • Patrizia Berti

    (Department of Mathematics, University of Modena and Reggio Emilia)

  • Luca Pratelli

    (Accademia Navale di Livorno)

  • Pietro Rigo

    (Department of Economics and Quantitative Methods, University of Pavia)

Abstract

Let L be a linear space of real bounded random variables on the probability space (omega,A, P0). There is a finitely additive probability P on A, such that P tilde P0 and EP (X) = 0 for all X in L, if and only if cEQ(X) = ess sup(-X), X in L, for some constant c > 0 and (countably additive) probability Q on A such that Q tilde P0. A necessary condition for such a P to exist is L - L+(inf) n L+(inf) = {0}, where the closure is in the norm-topology. If P0 is atomic, the condition is sufficient as well. In addition, there is a finitely additive probability P on A, such that P

Suggested Citation

  • Patrizia Berti & Luca Pratelli & Pietro Rigo, 2010. "Finitely Additive Equivalent Martingale Measures," Quaderni di Dipartimento 123, University of Pavia, Department of Economics and Quantitative Methods.
    • Handle: RePEc:pav:wpaper:123
    as

    Download full text from publisher

    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/wpaper/q123.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Patrizia Berti & Eugenio Regazzini & Pietro Rigo, 2001. "Strong previsions of random elements," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 11-28, January.
    2. Back, Kerry & Pliska, Stanley R., 1991. "On the fundamental theorem of asset pricing with an infinite state space," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 1-18.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2013. "Finitely Additive Equivalent Martingale Measures," Journal of Theoretical Probability, Springer, vol. 26(1), pages 46-57, March.
    2. Tak Siu & John Lau & Hailiang Yang, 2007. "On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(3), pages 255-275, September.
    3. Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
    4. Yao, Yong, 1999. "Term structure modeling and asymptotic long rate," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 327-336, December.
    5. Jaime A. Londo~no, 2003. "State Tameness: A New Approach for Credit Constrains," Papers math/0305274, arXiv.org, revised Feb 2004.
    6. Tak Siu, 2006. "Option Pricing Under Autoregressive Random Variance Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 62-75.
    7. Vantaggi, Barbara, 2010. "Incomplete preferences on conditional random quantities: Representability by conditional previsions," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 104-112, September.
    8. Gibson, Rajna & Lhabitant, Francois-Serge & Talay, Denis, 2010. "Modeling the Term Structure of Interest Rates: A Review of the Literature," Foundations and Trends(R) in Finance, now publishers, vol. 5(1–2), pages 1-156, December.
    9. Dilip B. Madan & Frank Milne, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 223-245, July.
    10. Mirás, Miguel Ángel & Muñoz-Bouzo, María José, 2001. "Projective system approach to the martingale characterization of the absence of arbitrage," DEE - Working Papers. Business Economics. WB wb011505, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    11. repec:dau:papers:123456789/5374 is not listed on IDEAS
    12. Balbás, Alejandro & Serna, Gregorio, 2024. "Selling options to beat the market: Further empirical evidence," Research in International Business and Finance, Elsevier, vol. 67(PB).
    13. Pierpaolo Angelini, 2020. "A Portfolio of Risky Assets and Its Intrinsic Properties," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(3), pages 1-61, June.
    14. Lau, John W. & Siu, Tak Kuen, 2008. "On option pricing under a completely random measure via a generalized Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 99-107, August.
    15. Sebastian del Bano Rollin & Zsolt Bihari & Tomaso Aste, 2018. "Risk-Neutral Pricing and Hedging of In-Play Football Bets," Papers 1811.03931, arXiv.org.
    16. Pierpaolo Angelini, 2024. "Extended Least Squares Making Evident Nonlinear Relationships between Variables: Portfolios of Financial Assets," JRFM, MDPI, vol. 17(8), pages 1-24, August.
    17. Siu, Tak Kuen, 2008. "A game theoretic approach to option valuation under Markovian regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1146-1158, June.
    18. Patrick Assonken & G. S. Ladde, 2015. "Option Pricing With A Levy-Type Stochastic Dynamic Model For Stock Price Process Under Semi-Markovian Structural Perturbations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-72, December.
    19. Hindy, Ayman, 1995. "Viable prices in financial markets with solvency constraints," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 105-135.
    20. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    21. repec:cte:wbrepe:wb043513 is not listed on IDEAS
    22. Mark J. Schervish & Teddy Seidenfeld & Joseph B. Kadane, 2014. "On the equivalence of conglomerability and disintegrability for unbounded random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 501-518, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pav:wpaper:123. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Paolo Bonomolo (email available below). General contact details of provider: https://edirc.repec.org/data/dppavit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.