标题： 打地鼠在线学习：日内隐波动率曲面的物理信息神经网络 显示英文标题

标题： Whack-a-mole Online Learning: Physics-Informed Neural Network for Intraday Implied Volatility Surface

摘要： 使用稀疏市场数据校准时间依赖的隐含波动率曲面（IVS）是计算金融中的一个关键挑战，特别是在实时应用中。 此任务不仅需要拟合市场数据，还需要满足由偏微分方程（PDE）和无套利条件（由微分不等式建模）指定的条件。 本文提出了一种称为Whack-a-mole在线学习（WamOL）的新颖物理信息神经网络（PINNs）方法，以解决这个多目标优化问题。 WamOL为每个损失项集成了自适应和自动平衡过程，高效地重新加权目标函数，以确保平滑的曲面拟合，同时遵守PDE和无套利约束，并用于日内预测。 在我们的实验中，WamOL在从不均匀和稀疏的市场数据校准日内IVS方面表现出色，有效地捕捉了期权价格及其相关风险概况的动态演变。 这种方法为日内IVS校准提供了一个高效的解决方案，扩展了PINNs的应用，并为实时金融建模提供了一种方法。 显示英文摘要

摘要： Calibrating the time-dependent Implied Volatility Surface (IVS) using sparse market data is an essential challenge in computational finance, particularly for real-time applications. This task requires not only fitting market data but also satisfying a specified partial differential equation (PDE) and no-arbitrage conditions modelled by differential inequalities. This paper proposes a novel Physics-Informed Neural Networks (PINNs) approach called Whack-a-mole Online Learning (WamOL) to address this multi-objective optimisation problem. WamOL integrates self-adaptive and auto-balancing processes for each loss term, efficiently reweighting objective functions to ensure smooth surface fitting while adhering to PDE and no-arbitrage constraints and updating for intraday predictions. In our experiments, WamOL demonstrates superior performance in calibrating intraday IVS from uneven and sparse market data, effectively capturing the dynamic evolution of option prices and associated risk profiles. This approach offers an efficient solution for intraday IVS calibration, extending PINNs applications and providing a method for real-time financial modelling.