论文标题
一种完全数据驱动的方法，可通过SGLD最大程度地减少资产投资组合的CVAR，并不连续更新
A fully data-driven approach to minimizing CVaR for portfolio of assets via SGLD with discontinuous updating
论文作者
论文摘要
通过使用随机梯度Langevin动力学（SGLD）算法，一种随机优化的新方法，该算法是随机梯度不错（SGD）方法的一种变体，使我们能够有效地近似于可能复杂，高维景观的全球最小化。考虑到这一点，我们将SGLD的非反应分析扩展到了不连续的随机梯度的情况。因此，我们能够为凸（标准）Wasserstein距离的算法汇合提供理论保证，均可为凸面和非核心目标函数提供（标准）的距离距离。我们还提供了与这些目标功能的全球最小化器近似相关的预期过量风险的明确估计。所有这些发现使我们能够设计并提出完全数据驱动的方法，以最佳分配权重，以最大程度地减少资产投资组合的CVAR，并具有完整的理论保证。数值结果说明了我们的主要发现。
A new approach in stochastic optimization via the use of stochastic gradient Langevin dynamics (SGLD) algorithms, which is a variant of stochastic gradient decent (SGD) methods, allows us to efficiently approximate global minimizers of possibly complicated, high-dimensional landscapes. With this in mind, we extend here the non-asymptotic analysis of SGLD to the case of discontinuous stochastic gradients. We are thus able to provide theoretical guarantees for the algorithm's convergence in (standard) Wasserstein distances for both convex and non-convex objective functions. We also provide explicit upper estimates of the expected excess risk associated with the approximation of global minimizers of these objective functions. All these findings allow us to devise and present a fully data-driven approach for the optimal allocation of weights for the minimization of CVaR of portfolio of assets with complete theoretical guarantees for its performance. Numerical results illustrate our main findings.
