Kernel Ridge Regression

Transfer Learning Across Fixed-Income Product Classes ArXiv ID: 2505.07676 “View on arXiv” Authors: Nicolas Camenzind, Damir Filipovic Abstract We propose a framework for transfer learning of discount curves across different fixed-income product classes. Motivated by challenges in estimating discount curves from sparse or noisy data, we extend kernel ridge regression (KR) to a vector-valued setting, formulating a convex optimization problem in a vector-valued reproducing kernel Hilbert space (RKHS). Each component of the solution corresponds to the discount curve implied by a specific product class. We introduce an additional regularization term motivated by economic principles, promoting smoothness of spread curves between product classes, and show that it leads to a valid separable kernel structure. A main theoretical contribution is a decomposition of the vector-valued RKHS norm induced by separable kernels. We further provide a Gaussian process interpretation of vector-valued KR, enabling quantification of estimation uncertainty. Illustrative examples demonstrate that transfer learning significantly improves extrapolation performance and tightens confidence intervals compared to single-curve estimation. ...

A Multi-step Approach for Minimizing Risk in Decentralized Exchanges ArXiv ID: 2406.07200 “View on arXiv” Authors: Unknown Abstract Decentralized Exchanges are becoming even more predominant in today’s finance. Driven by the need to study this phenomenon from an academic perspective, the SIAG/FME Code Quest 2023 was announced. Specifically, participating teams were asked to implement, in Python, the basic functions of an Automated Market Maker and a liquidity provision strategy in an Automated Market Maker to minimize the Conditional Value at Risk, a critical measure of investment risk. As the competition’s winning team, we highlight our approach in this work. In particular, as the dependence of the final return on the initial wealth distribution is highly non-linear, we cannot use standard ad-hoc approaches. Additionally, classical minimization techniques would require a significant computational load due to the cost of the target function. For these reasons, we propose a three-step approach. In the first step, the target function is approximated by a Kernel Ridge Regression. Then, the approximating function is minimized. In the final step, the previously discovered minimum is utilized as the starting point for directly optimizing the desired target function. By using this procedure, we can both reduce the computational complexity and increase the accuracy of the solution. Finally, the overall computational load is further reduced thanks to an algorithmic trick concerning the returns simulation and the usage of Cython. ...