Market Viability and Martingale Measures under Partial Information

作者：Fontana Claudio; Oksendal Bernt^*; Sulem Agnes

来源：Methodology and Computing in Applied Probability, 2015, 17(1): 15-39.

DOI：10.1007/s11009-014-9397-4

• Optimal portfolio
• Jump-diffusion
• Partial information
• Maximum principle
• BSDE
• Viability
• Utility maximization
• Martingale measure
• Martingale deflator

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.

• 出版日期2015-3
• 单位INRIA