Pathwise Dynamic Programming
提出一种新方法，为随机动态规划方程的解构建紧的蒙特卡洛置信区间，通过构造已知偏差的路径递归并耦合上下界，适用于不满足比较原理的动态规划，并应用于双边对手风险、不确定波动率和协商抵押品下的非线性期权定价。
We present a novel method for deriving tight Monte Carlo confidence intervals for solutions of stochastic dynamic programming equations. Taking some approximate solution to the equation as an input, we construct pathwise recursions with a known bias. Suitably coupling the recursions for lower and upper bounds ensures that the method is applicable even when the dynamic program does not satisfy a comparison principle. We apply our method to three nonlinear option pricing problems, pricing under bilateral counterparty risk, under uncertain volatility, and under negotiated collateralization.