论文速递|Management Science 6月文章合集

We investigate the optimal clearing policy for a financial payment system composed of a number of member banks and a central bank in a dynamic setting, when new payment obligations or debts between member banks are generated over time. The central bank clears the debts among members in the system in order to minimize the costs, including the setup cost of each clearing, the variable cost of clearing the net debts, and the liquidity cost of uncleared debts. We formulate the problem using dynamic programming via state space reduction that provides a tractable framework to analyze and compute the optimal policy. We characterize the structure of the optimal policy and show that it is optimal for the central bank either to clear all the debts in the system or not to clear at all in each period under mild conditions. This structure leads to efficient computation of the optimal clearing policy. We further characterize the optimal clearing frequency based upon the deterministic approximation for the debt process. We conduct a comprehensive case study based on the data acquired from our industry partner, Payments Canada, to demonstrate the performance of the policy and its feasibility in industrial-size problems.

我们研究了一个由多家成员银行和中央银行组成的金融支付系统在动态环境中的最佳清算政策，当成员银行之间随时间产生新的支付义务或债务时。中央银行在系统中清算成员之间的债务，以最小化成本，包括每次清算的设置成本、清算净债务的变动成本，以及未清算债务的流动性成本。我们通过状态空间缩减使用动态规划来制定问题，这提供了一个可行的框架来分析和计算最佳政策。我们描述了最佳政策的结构，并表明在轻微条件下，中央银行在每个时期要么清算系统中的所有债务，要么根本不清算是最优的。这种结构导致最佳清算政策的高效计算。我们进一步基于债务过程的确定性近似来描述最佳清算频率。我们基于我们的行业合作伙伴加拿大支付公司提供的数据进行了全面的案例研究，以展示政策的性能及其在工业规模问题中的可行性。

Transition probability density functions (TPDFs) are fundamental to computational finance, including option pricing and hedging. Advancing recent work in deep learning, we develop novel neural TPDF generators through solving backward Kolmogorov equations in parametric space for cumulative probability functions. The generators are ultra-fast, very accurate and can be trained for any asset model described by stochastic differential equations. These are “single solve,” so they do not require retraining when parameters of the stochastic model are changed (e.g., recalibration of volatility). Once trained, the neural TDPF generators can be transferred to less powerful computers where they can be used for e.g. option pricing at speeds as fast as if the TPDF were known in a closed form. We illustrate the computational efficiency of the proposed neural approximations of TPDFs by inserting them into numerical option pricing methods. We demonstrate a wide range of applications including the Black-Scholes-Merton model, the standard Heston model, the SABR model, and jump-diffusion models. These numerical experiments confirm the ultra-fast speed and high accuracy of the developed neural TPDF generators.

转移概率密度函数（TPDFs）对计算金融至关重要，包括期权定价和对冲。在深度学习的最新工作基础上，我们开发了新颖的神经TPDF生成器，通过解决累积概率函数的参数空间中的逆向Kolmogorov方程。这些生成器超快速、非常准确，并且可以训练用于任何由随机微分方程描述的资产模型。它们是“一次性求解”，因此当随机模型的参数变化时（例如，波动率的重新校准），不需要重新训练。一旦训练完成，神经TPDF生成器可以转移到计算能力较低的计算机上，它们可以用于例如期权定价，速度几乎与TPDF已知的封闭形式一样快。我们通过将所提出的神经近似TPDFs插入到数值期权定价方法中，展示了所提出神经近似TPDFs的计算效率。我们展示了广泛的应用，包括Black-Scholes-Merton模型、标准Heston模型、SABR模型和跳跃扩散模型。这些数值实验证实了所开发的神经TPDF生成器的超快速度和高准确性。