Generative Bayesian Computation (GBC) methods are developed to provide an efficient computational solution for maximum expected utility (MEU). We propose a density-free generative method based on quantiles that naturally calculates expected utility as a marginal of quantiles. Our approach uses a deep quantile neural estimator to directly estimate distributional utilities. Generative methods assume only the ability to simulate from the model and parameters and as such are likelihood-free. A large training dataset is generated from parameters and output together with a base distribution. Our method a number of computational advantages primarily being density-free with an efficient estimator of expected utility. A link with the dual theory of expected utility and risk taking is also discussed. To illustrate our methodology, we solve an optimal portfolio allocation problem with Bayesian learning and a power utility (a.k.a. fractional Kelly criterion). Finally, we conclude with directions for future research.

翻译：本文提出生成式贝叶斯计算方法，旨在为最大期望效用问题提供高效的计算解决方案。我们基于分位数提出一种无密度生成方法，该方法通过分位数的边际分布自然计算期望效用。我们的方法采用深度分位数神经网络估计器直接估计分布效用。生成式方法仅需假设能够从模型和参数中进行模拟，因此属于免似然方法。我们通过参数与输出数据及基础分布生成大规模训练数据集。该方法具有多项计算优势，主要包括无密度特性及高效的期望效用估计器。文中同时探讨了该方法与期望效用对偶理论及风险承担行为的关联。为验证方法有效性，我们结合贝叶斯学习与幂效用函数（亦称分数凯利准则）解决了最优投资组合配置问题。最后，本文提出了未来研究方向。