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Market Viability and Martingale Measures under Partial Information

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Listed:
  • Claudio Fontana

    (INRIA Paris-Rocquencourt)

  • Bernt Øksendal

    (Université Paris-Est)

  • Agnès Sulem

    (INRIA Paris-Rocquencourt)

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.

Suggested Citation

  • Claudio Fontana & Bernt Øksendal & Agnès Sulem, 2015. "Market Viability and Martingale Measures under Partial Information," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 15-39, March.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:1:d:10.1007_s11009-014-9397-4
    DOI: 10.1007/s11009-014-9397-4
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    References listed on IDEAS

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