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Market viability and martingale measures under partial information

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  • Claudio Fontana
  • Bernt {\O}ksendal
  • Agn\`es Sulem
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    Abstract

    We consider a financial market model with a single risky asset whose price process evolves according to a general jump-diffusion with locally bounded coefficients and where market participants have only access to a partial information flow. For any utility function, we prove that the partial information financial market is locally viable, in the sense that the optimal portfolio problem has a solution up to a stopping time, if and only if the (normalised) marginal utility of the terminal wealth generates a partial information equivalent martingale measure (PIEMM). This equivalence result is proved in a constructive way by relying on maximum principles for stochastic control problems under partial information. We then characterize a global notion of market viability in terms of partial information local martingale deflators (PILMDs). We illustrate our results by means of a simple example.

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    File URL: http://arxiv.org/pdf/1302.4254
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1302.4254.

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    Date of creation: Feb 2013
    Date of revision: Oct 2013
    Handle: RePEc:arx:papers:1302.4254

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    1. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    2. Mark Loewenstein & Gregory A. Willard, 2000. "Local martingales, arbitrage, and viability," Economic Theory, Springer, vol. 16(1), pages 135-161.
    3. Björk, Tomas & Davis, Mark H.A. & Landén, Camilla, 2010. "Optimal Investment under Partial Information," Working Paper Series in Economics and Finance 739, Stockholm School of Economics.
    4. Jan Ubøe & Bernt Øksendal & Knut Aase & Nicolas Privault, 2000. "White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance," Finance and Stochastics, Springer, vol. 4(4), pages 465-496.
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