Inspired by Strotz's consistent planning strategy, we formulate the infinite horizon mean-variance stopping problem as a subgame perfect Nash equilibrium in order to determine time consistent strategies with no regret. Equilibria among stopping times or randomized stopping times may not exist....

Oft-cited causes of mini-flash crashes include human errors, endogenous feedback loops, the nature of modern liquidity provision, fundamental value shocks, and market fragmentation. We develop a mathematical model which captures aspects of the first three explanations. Empirical features of...

We solve the martingale optimal transport problem for cost functionals represented by optimal stopping problems. The measure-valued martingale approach developed in [A. M. G. Cox and S. Kallblad. Model-independent bounds for Asian options: a dynamic programming approach. SIAM Journal on Control...

In this paper we develop two numerical methods for optimal stopping in the framework of one dimensional diffusion. Both of the methods use the Skorohod embedding in order to construct recombining tree approximations for diffusions with general coefficients. This technique allows us to determine...

We discuss a natural game of competition and solve the corresponding mean field game with common noise when agents' rewards are rank-dependent. We use this solution to provide an approximate Nash equilibrium for the finite player game and obtain the rate of convergence

We consider the optimal dividend problem under a habit formation constraint that prevents the dividend rate to fall below a certain proportion of its historical maximum, the so-called drawdown constraint. This is an extension of the optimal Duesenberry's ratcheting consumption problem, studied...