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 pr...

We give short proofs of general theorems about optimal entry and exit problems in Lévy models, when payoff streams may have discontinuities and be non-monotone. As applications, we consider exit and entry problems in the theory of real options, and an entry problem with an embedded option to exit.

The paper deals with the quickest detection of intensity change for Poisson process. We show that the generalized Bayesian formulation of the quickest detection problem can be reduced to the conditional-extremal optimal stopping problem for a piecewise-deterministic Markov process. For this problem the optimal procedure is described and its characteristics are found.