Primal and dual optimal stopping with signatures
提出两种基于路径签名的方法，用于非马尔可夫框架下的最优停止问题（如美式期权定价），分别推广了Longstaff-Schwartz算法和利用签名线性泛函参数化鞅空间，并证明了收敛性。
Abstract We propose two signature-based methods to solve an optimal stopping problem – that is, to price American options – in non-Markovian frameworks. Both methods rely on a global approximation result for $L^{p}$ L p -functionals on rough-path spaces, using linear functionals of robust, rough-path signatures. In the primal formulation, we present a non-Markovian generalisation of the famous Longstaff–Schwartz algorithm, using linear functionals of the signature as regression basis. For the dual formulation, we parametrise the space of square-integrable martingales using linear functionals of the signature and apply a sample average approximation. We prove convergence for both methods and present first numerical examples in non-Markovian and non-semimartingale regimes.