Market Viability and Martingale Measures under Partial Information

Claudio Fontana (), Bernt Øksendal () and Agnès Sulem ()
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Claudio Fontana: INRIA Paris-Rocquencourt
Bernt Øksendal: Université Paris-Est
Agnès Sulem: INRIA Paris-Rocquencourt

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 1, 15-39

Abstract: 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.

Keywords: Optimal portfolio; Jump-diffusion; Partial information; Maximum principle; BSDE; Viability; Utility maximization; Martingale measure; Martingale deflator; 60G44; 60G51; 60G57; 91B70; 91G80; 93E20; 94A17 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-014-9397-4

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