This paper proposes an approximation method to create an optimal continuous-time portfolio strategy based on a combination of neural networks and Monte Carlo, named NNMC. This work is motivated by the increasing complexity of continuous-time models and stylized facts reported in the literature. We work within expected utility theory for portfolio selection with constant relative risk aversion utility. The method extends a recursive polynomial exponential approximation framework by adopting neural networks to fit the portfolio value function. We developed two network architectures and explored several activation functions. The methodology was applied on four settings: a 4/2 stochastic volatility (SV) model with two types of market price of risk, a 4/2 model with jumps, and an Ornstein–Uhlenbeck 4/2 model. In only one case, the closed-form solution was available, which helps for comparisons. We report the accuracy of the various settings in terms of optimal strategy, portfolio performance and computational efficiency, highlighting the potential of NNMC to tackle complex dynamic models.

中文翻译：

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期望效用理论的神经网络蒙特卡罗近似

本文提出了一种近似方法来创建基于神经网络和蒙特卡罗组合的最优连续时间投资组合策略，称为 NNMC。这项工作的动机是连续时间模型和文献中报道的程式化事实越来越复杂。我们在期望效用理论中使用恒定的相对风险厌恶效用进行投资组合选择。该方法通过采用神经网络来拟合投资组合价值函数，扩展了递归多项式指数逼近框架。我们开发了两种网络架构并探索了几个激活函数。该方法应用于四种设置：具有两种风险市场价格的 4/2 随机波动率 (SV) 模型、具有跳跃的 4/2 模型和 Ornstein-Uhlenbeck 4/2 模型。只有一种情况，可以使用封闭形式的解决方案，这有助于进行比较。我们报告了各种设置在最佳策略、投资组合性能和计算效率方面的准确性，突出了 NNMC 处理复杂动态模型的潜力。