Raphael Douady

Siqiao Zhao, Zhikang Dong, Zeyu Cao et al.

When constructing portfolios, a key problem is that a lot of financial time series data are sparse, making it challenging to apply machine learning methods. Polymodel theory can solve this issue and demonstrate superiority in portfolio construction from various aspects. To implement the PolyModel theory for constructing a hedge fund portfolio, we begin by identifying an asset pool, utilizing over 10,000 hedge funds for the past 29 years' data. PolyModel theory also involves choosing a wide-ranging set of risk factors, which includes various financial indices, currencies, and commodity prices. This comprehensive selection mirrors the complexities of the real-world environment. Leveraging on the PolyModel theory, we create quantitative measures such as Long-term Alpha, Long-term Ratio, and SVaR. We also use more classical measures like the Sharpe ratio or Morningstar's MRAR. To enhance the performance of the constructed portfolio, we also employ the latest deep learning techniques (iTransformer) to capture the upward trend, while efficiently controlling the downside, using all the features. The iTransformer model is specifically designed to address the challenges in high-dimensional time series forecasting and could largely improve our strategies. More precisely, our strategies achieve better Sharpe ratio and annualized return. The above process enables us to create multiple portfolio strategies aiming for high returns and low risks when compared to various benchmarks.

Lingjie Yi, Raphael Douady, Chao Chen

Multimodal contrastive learning (MCL) aims to embed data from different modalities in a shared embedding space. However, empirical evidence shows that representations from different modalities occupy completely separate regions of embedding space, a phenomenon referred to as the modality gap. Moreover, experimental findings on how the size of the modality gap influences downstream performance are inconsistent. These observations raise two key questions: (1) What causes the modality gap? (2) How does it affect downstream tasks? To address these questions, this paper introduces the first theoretical framework for analyzing the convergent optimal representations of MCL and the modality alignment when training is optimized. Specifically, we prove that without any constraint or under the cone constraint, the modality gap converges to zero. Under the subspace constraint (i.e., representations of two modalities fall into two distinct hyperplanes due to dimension collapse), the modality gap converges to the smallest angle between the two hyperplanes. This result identifies \emph{dimension collapse} as the fundamental origin of the modality gap. Furthermore, our theorems demonstrate that paired samples cannot be perfectly aligned under the subspace constraint. The modality gap influences downstream performance by affecting the alignment between sample pairs. We prove that, in this case, perfect alignment between two modalities can still be achieved via two ways: hyperplane rotation and shared space projection.

Raphael Douady, Shohruh Miryusupov

We show the application of an optimal transportation approach to estimate stochastic volatility process by using the flow that optimally transports the set of particles from the prior to a posterior distribution. We also show how to direct the flow to a rarely visited areas of the state space by using a particle method (a mutation and a reweighing mechanism). We demonstrate the efficiency of our approach on a simple example of the European option price under the Stein-Stein stochastic volatility model for which a closed form formula is available. Both homotopy and reweighted homotopy methods show a lower variance, root-mean squared errors and a bias compared to other filtering schemes recently developed in the signal-processing literature, including particle filter techniques.