Market viability and martingale measures under partial information
AbstractWe 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1302.4254.
Date of creation: Feb 2013
Date of revision: Oct 2013
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- 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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- 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.
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