论文标题
MartingaleSchrödinger桥和最佳的半明上投资组合
Martingale Schrödinger Bridges and Optimal Semistatic Portfolios
论文作者
论文摘要
在一个两周期的金融市场，该市场动态交易股票并静态交易欧洲的期权，我们研究了所谓的Martingaleshrödinger桥Q*；也就是说，在所有校准期权价格的模型中，最小的室内群量措施。这种最小化证明是双重性的，对半上位投资组合的指数效用最大化。在物理度量P的技术条件下，我们表明存在最佳投资组合，并为Q*提供了明确的解决方案。该结果克服了Acciaio，Larsson和Schachermayer发现的半明上策略的非关闭性问题。具体而言，我们展示了具有特定特性的校准的校准措施的密集子集，以表明所讨论的投资组合具有明确且可集成的选项位置。
In a two-period financial market where a stock is traded dynamically and European options at maturity are traded statically, we study the so-called martingale Schrödinger bridge Q*; that is, the minimal-entropy martingale measure among all models calibrated to option prices. This minimization is shown to be in duality with an exponential utility maximization over semistatic portfolios. Under a technical condition on the physical measure P, we show that an optimal portfolio exists and provides an explicit solution for Q*. This result overcomes the remarkable issue of non-closedness of semistatic strategies discovered by Acciaio, Larsson and Schachermayer. Specifically, we exhibit a dense subset of calibrated martingale measures with particular properties to show that the portfolio in question has a well-defined and integrable option position.
