论文标题
跳高的BSDE的深层求解器
A deep solver for BSDEs with jumps
论文作者
论文摘要
这项工作的目的是提出Han，Jentzen，E（2018）将深层求解器扩展到具有跳跃向前向后的随机微分方程（FBSDE）的情况。就像在上述求解器中一样，从fbsde的离散版本开始，并通过人工神经网络（ANN）家族来对（高维）控制过程进行参数化，将FBSDE视为基于模型的增强性学习问题，并将ANN参数视为最小化处方损失功能的ANN参数。我们通过引入有限的近似值来考虑有限和无限的跳跃活动，并具有有限的前进过程跳跃。我们成功地将算法应用于低维度和高维度的期权定价问题，并在交易对手信用风险的情况下讨论适用性。
The aim of this work is to propose an extension of the deep solver by Han, Jentzen, E (2018) to the case of forward backward stochastic differential equations (FBSDEs) with jumps. As in the aforementioned solver, starting from a discretized version of the FBSDE and parametrizing the (high dimensional) control processes by means of a family of artificial neural networks (ANNs), the FBSDE is viewed as a model-based reinforcement learning problem and the ANN parameters are fitted so as to minimize a prescribed loss function. We take into account both finite and infinite jump activity by introducing, in the latter case, an approximation with finitely many jumps of the forward process. We successfully apply our algorithm to option pricing problems in low and high dimension and discuss the applicability in the context of counterparty credit risk.
