Solving optimal stopping problems under model uncertainty via empirical dual optimisation
研究在模型不确定下求解最优停止问题，基于对偶表示开发了回归蒙特卡洛算法，通过优化惩罚经验对偶目标函数构造上界，并进行了收敛性分析和数值验证。
Abstract In this work, we consider optimal stopping problems with model uncertainty incorporated into the formulation of the underlying objective function. Typically, the robust, efficient hedging of American options in incomplete markets may be described as optimal stopping of such kind. Based on a generalisation of the additive dual representation of Rogers (Math. Financ. 12:271–286, 2002) to the case of optimal stopping under model uncertainty, we develop a novel regression-based Monte Carlo algorithm for the approximation of the corresponding value function. The algorithm involves optimising a penalised empirical dual objective functional over a class of martingales. This formulation allows us to construct upper bounds for the optimal value with reduced complexity. Finally, we carry out a convergence analysis of the proposed algorithm and illustrate its performance by several numerical examples.