Supermartingale deflators in the absence of a numéraire

Filtration shrinkage, the structure of deflators, and failure of market completeness

We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale part in the multiplicative Doob-Meyer decomposition of projected local martingale deflators are themselves local martingale deflators in the smaller information market. Via use of a Bayesian filtering approach, we demonstrate the exact mechanism of how updates on the possible class of models under less information result in the strict supermartingale property of projections of such deflators. Finally, we demonstrate that these projecti…

On the Existence of Martingale Measures in Jump Diffusion Market Models

In the context of jump-diffusion market models we construct examples that satisfy the weaker no-arbitrage condition of NA1 (NUPBR), but not NFLVR. We show that in these examples the only candidate for the density process of an equivalent local martingale measure is a supermartingale that is not a martingale, not even a local martingale. This candidate is given by the supermartingale deflator resulting from the inverse of the discounted growth optimal portfolio. In particular, we con- sider an example with constraints on the portfolio that go beyond the standard ones for admissibility.

无风险影子利率的经验实现

An Empirical Implementation of the Shadow Riskless Rate

本文针对无无风险资产市场，基于几何布朗运动假设，开发了一种结合主成分分析、奇异值分解和正则化的计算方法，从经验数据估计无风险影子利率（SRR）及其状态价格平减因子的漂移和波动率。

随机维数市场中的套利理论

Arbitrage theory in a market of stochastic dimension

本文研究资产数量随时间波动的随机维数股票市场，建立资产定价基本定理与可选分解定理，并推广至开放市场，刻画无套利条件与计价单位组合。

无套利与乘法特殊半鞅

No arbitrage and multiplicative special semimartingales

本文研究无计价单位的非负半鞅金融市场，证明在允许添加储蓄账户的意义下，市场无套利当且仅当存在作为乘法特殊半鞅的等价局部鞅平减指数，并揭示储蓄账户与平减指数乘法分解的有限变差部分之间的对应关系。