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Market Viability and Martingale Measures under Partial Information

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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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Author notes

  1. Claudio Fontana

    Present address: University of Évry, 23 bd de France, Évry, 91037, France

Authors and Affiliations

  1. INRIA Paris-Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, Le Chesnay Cedex, 78153, France

    Claudio Fontana & Agnès Sulem

  2. Université Paris-Est, F-77455, Marne-la-Vallée, France

    Bernt Øksendal

Authors
  1. Claudio Fontana
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  2. Bernt Øksendal
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  3. Agnès Sulem
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Correspondence to Bernt Øksendal.

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Fontana, C., Øksendal, B. & Sulem, A. Market Viability and Martingale Measures under Partial Information. Methodol Comput Appl Probab 17, 15–39 (2015). https://doi.org/10.1007/s11009-014-9397-4

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  • DOI: https://doi.org/10.1007/s11009-014-9397-4

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