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Market viability and martingale measures under partial information

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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https://hal.archives-ouvertes.fr/hal-01171646
Contributor : Serena Benassù <>
Submitted on : Monday, July 6, 2015 - 10:10:51 AM
Last modification on : Thursday, April 16, 2020 - 4:00:05 PM

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C. Fontana, B. Oksendal, A. Sulem. Market viability and martingale measures under partial information. Methodology and Computing in Applied Probability, Springer Verlag, 2015, 17 (1), pp.15-39. ⟨10.1007/s11009-014-9397-4⟩. ⟨hal-01171646⟩

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