Optimal stopping with signatures

We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process X. consider classic and randomized times represented by linear nonlinear functionals of rough path signature X<∞ associated to X, prove that maximizing over these classes times, fact, solves original problem. Using algebraic properties signature, we can then recast problem (deterministic) optimization depending only (truncated) expected E[X0,T≤N]. By applying deep neural network approach approximate functionals, efficiently solve numerically. The assumption X is it continuous (geometric) random path. Hence, theory encompasses processes such fractional Brownian motion, which fail be either semimartingales or Markov processes, used, particular, American-type models, example, financial electricity markets.