Market viability and martingale measures under partial information

Claudio Fontana, Bernt {\O}ksendal and Agn\`es Sulem

Papers from arXiv.org

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.

Date: 2013-02, Revised 2013-10
New Economics Papers: this item is included in nep-upt
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Published in Methodology and Computing in Applied Probability, 2015, vol. 17(1), 15-39

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