部分信息下的市场生存与鞅测度
Market viability and martingale measures under partial information
摘要：
考虑一个金融市场模型，其中风险资产的价格过程服从系数局部有界的一般跳扩散过程，且市场参与者只能获得部分信息流.对于任何效用函数，我们证明了部分信息的金融市场是局部可行的，在这个意义上，最优投资组合问题有一个解决方案的停时，当且仅当（归一化）的边际效用的终端财富产生部分信息等价鞅测度（PIEMM）。借助于部分信息下随机控制问题的极大值原理，构造性地证明了这一等价结果。然后，我们描述了一个全球性的概念，市场生存能力的部分信息本地鞅平减指数（PILMDs）。我们通过一个简单的例子来说明我们的结果。
英文摘要：
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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