论文标题
基于双重性的某些近似方案的后验误差估计，用于最佳投资问题
Duality-based a posteriori error estimates for some approximation schemes for optimal investment problems
论文作者
论文摘要
我们考虑了Markov链近似方案，用于连续时间的实用性最大化问题，该方案又使用了分段恒定的策略近似，Euler-Maruyama Time Stepping和高斯增量的高斯 - 甲酸盐近似。先前在Picarelli和Reisinger（2019）中得出的误差估计值是由于控制近似而在上限和上限之间不对称，并且仅在较低情况下在文献中改善了已知结果。在本文中，我们使用二元性结果获得后验误差边界，在经验上，该误差与下限相同。理论结果通过我们的数值测试证实。
We consider a Markov chain approximation scheme for utility maximization problems in continuous time, which uses, in turn, a piecewise constant policy approximation, Euler-Maruyama time stepping, and a Gauss-Hermite approximation of the Gaussian increments. The error estimates previously derived in Picarelli and Reisinger (2019) are asymmetric between lower and upper bounds due to the control approximation and improve on known results in the literature in the lower case only. In the present paper, we use duality results to obtain a posteriori upper error bounds which are empirically of the same order as the lower bounds. The theoretical results are confirmed by our numerical tests.
